Premise #2: When all men are cowards, there will be no war.
Conclusion: When all men are wealthy, there will be no war.
Reasons to Believe Premise #1: Richer countries are much less violent than poor countries; within countries, the rich are much less violent than the poor. Also, in rich countries, small numbers of casualties seem to have large negative effects on public support for war. (My main qualification: It may take a generation or two for the cowardice to kick in. There is probably a gradual social multiplier effect that amplifies the change in individual behavior).
Reasons to Believe Premise #2: This seems obvious enough. However, game theorists will tell you that matters are a little more complicated. When everyone else is a coward, even a coward can safely become a bully. In the real world, though, a small probability that a cowardly victim will defend himself will be enough to deter a cowardly bully.
Upshot: Since there is every reason to expect economic growth to continue throughout the world, world peace is probably only a few generations away.