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Theorem u2lemnana 646
Description: Lemma for Dishkant implication study.
Assertion
Ref Expression
u2lemnana ((a ->2 b)' ^ a') = 0
Proof of Theorem u2lemnana
StepHypRef Expression
1 anor3 90 . . 3 ((a ->2 b)' ^ a') = ((a ->2 b) v a)'
2 u2lemoa 621 . . . 4 ((a ->2 b) v a) = 1
32ax-r4 37 . . 3 ((a ->2 b) v a)' = 1'
41, 3ax-r2 36 . 2 ((a ->2 b)' ^ a') = 1'
5 df-f 42 . . 3 0 = 1'
65ax-r1 35 . 2 1' = 0
74, 6ax-r2 36 1 ((a ->2 b)' ^ a') = 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-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:  u2lem5  762
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