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Theorem pm2.61ne 2591
Description: Deduction eliminating an inequality in an antecedent. (Contributed by NM, 24-May-2006.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypotheses
Ref Expression
pm2.61ne.1
pm2.61ne.2
pm2.61ne.3
Assertion
Ref Expression
pm2.61ne

Proof of Theorem pm2.61ne
StepHypRef Expression
1 pm2.61ne.2 . . 3
21expcom 424 . 2
3 nne 2520 . . 3
4 pm2.61ne.3 . . . 4
5 pm2.61ne.1 . . . 4
64, 5syl5ibr 212 . . 3
73, 6sylbi 187 . 2
82, 7pm2.61i 156 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176   wa 358   wceq 1642   wne 2516
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-ne 2518
This theorem is referenced by: (None)
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