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Theorem u4lembi 724
Description: Non-tollens implication and biconditional.
Assertion
Ref Expression
u4lembi ((a ->4 b) ^ (b ->4 a)) = (a == b)
Proof of Theorem u4lembi
StepHypRef Expression
1 ud4lem1a 577 . 2 ((a ->4 b) ^ (b ->4 a)) = ((a ^ b) v (a' ^ b'))
2 dfb 94 . . 3 (a == b) = ((a ^ b) v (a' ^ b'))
32ax-r1 35 . 2 ((a ^ b) v (a' ^ b')) = (a == b)
41, 3ax-r2 36 1 ((a ->4 b) ^ (b ->4 a)) = (a == b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5   v wo 6   ^ wa 7   ->4 wi4 15
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i4 47  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
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