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Theorem wcon3 209
Description: Weak contraposition.
Hypothesis
Ref Expression
wcon3.1 (a' == b) = 1
Assertion
Ref Expression
wcon3 (a == b') = 1
Proof of Theorem wcon3
StepHypRef Expression
1 ax-a1 30 . . . . 5 b = b''
21ax-r1 35 . . . 4 b'' = b
32lbi 97 . . 3 (a' == b'') = (a' == b)
4 wcon3.1 . . 3 (a' == b) = 1
53, 4ax-r2 36 . 2 (a' == b'') = 1
65wcon1 207 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:  wlecon  395  wcomd  418  wfh1  423
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