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Theorem wcon2 208
Description: Weak contraposition.
Hypothesis
Ref Expression
wcon2.1 (a == b') = 1
Assertion
Ref Expression
wcon2 (a' == b) = 1
Proof of Theorem wcon2
StepHypRef Expression
1 conb 122 . . 3 (a' == b) = (a'' == b')
2 ax-a1 30 . . . . 5 a = a''
32rbi 98 . . . 4 (a == b') = (a'' == b')
43ax-r1 35 . . 3 (a'' == b') = (a == b')
51, 4ax-r2 36 . 2 (a' == b) = (a == b')
6 wcon2.1 . 2 (a == b') = 1
75, 6ax-r2 36 1 (a' == b) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5  1wt 8
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-b 39  df-a 40
This theorem is referenced by:  wcomlem  382  wcomd  418  wcomdr  421  wcom3i  422  wfh1  423  wfh2  424
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