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Theorem u2lemnab 651
Description: Lemma for Dishkant implication study.
Assertion
Ref Expression
u2lemnab ((a ->2 b)' ^ b) = 0
Proof of Theorem u2lemnab
StepHypRef Expression
1 u2lemonb 636 . . 3 ((a ->2 b) v b') = 1
2 oran1 91 . . 3 ((a ->2 b) v b') = ((a ->2 b)' ^ b)'
3 df-f 42 . . . . 5 0 = 1'
43con2 67 . . . 4 0' = 1
54ax-r1 35 . . 3 1 = 0'
61, 2, 53tr2 64 . 2 ((a ->2 b)' ^ b)' = 0'
76con1 66 1 ((a ->2 b)' ^ b) = 0
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8  0wf 9   ->2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i2 45
This theorem is referenced by: (None)
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