  Lower bounds are derived on the amplitude B of intergalactic magnetic fields
(IGMFs) in the region between Galaxy and the blazar Mrk 421, from constraints
on the delayed GeV pair-echo flux that are emitted by secondary e^-e^+ produced
in \gamma\gamma interactions between primary TeV gamma-rays and the cosmic
infrared background. The distribution of galaxies mapped by the Sloan Digital
Sky Survey shows that this region is dominated by a large intergalactic void.
We utilize data from long-term, simultaneous GeV-TeV observations by the Fermi
Large Area Telescope and the ARGO-YBJ experiment extending over 850 days. For
an assumed value of B, we evaluate the daily GeV pair-echo flux expected from
the TeV data, select the dates where this exceeds the Fermi 2-\sigma
sensitivity, compute the probability that this flux is excluded by the Fermi
data for each date, and then combine the probabilities using the inverse normal
method. Consequently, we exclude B < 10^{-20.5} G for a field coherence length
of 1 kpc at 4- \sigma level, as long as plasma instabilities are unimportant
for cooling of the pair beam. This is much more significant than the 2-\sigma
bounds we obtained previously from observations of Mrk 501, by virtue of more
extensive data from the ARGO-YBJ, as well as improved statistical analysis.
Compared with most other studies of IGMF bounds, the evidence we present here
for a non-zero IGMF is more robust as it does not rely on unproven assumptions
on the primary TeV emission during unobserved periods.
