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Theorem u2lemab 611
Description: Lemma for Dishkant implication study.
Assertion
Ref Expression
u2lemab ((a ->2 b) ^ b) = b
Proof of Theorem u2lemab
StepHypRef Expression
1 df-i2 45 . . 3 (a ->2 b) = (b v (a' ^ b'))
21ran 78 . 2 ((a ->2 b) ^ b) = ((b v (a' ^ b')) ^ b)
3 ancom 74 . . 3 ((b v (a' ^ b')) ^ b) = (b ^ (b v (a' ^ b')))
4 anabs 121 . . 3 (b ^ (b v (a' ^ b'))) = b
53, 4ax-r2 36 . 2 ((b v (a' ^ b')) ^ b) = b
62, 5ax-r2 36 1 ((a ->2 b) ^ b) = b
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i2 45
This theorem is referenced by:  u2lemnonb  676  u21lembi  727  bi3  839  bi4  840
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