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Theorem ud3lem3a 572
Description: Lemma for unified disjunction.
Assertion
Ref Expression
ud3lem3a ((a ->3 b)' ^ (a v b)) = (a ->3 b)'
Proof of Theorem ud3lem3a
StepHypRef Expression
1 ud3lem0c 279 . . 3 (a ->3 b)' = (((a v b') ^ (a v b)) ^ (a' v (a ^ b')))
2 lea 160 . . . 4 (((a v b') ^ (a v b)) ^ (a' v (a ^ b'))) =< ((a v b') ^ (a v b))
3 lear 161 . . . 4 ((a v b') ^ (a v b)) =< (a v b)
42, 3letr 137 . . 3 (((a v b') ^ (a v b)) ^ (a' v (a ^ b'))) =< (a v b)
51, 4bltr 138 . 2 (a ->3 b)' =< (a v b)
65df2le2 136 1 ((a ->3 b)' ^ (a v b)) = (a ->3 b)'
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->3 wi3 14
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i3 46  df-le1 130  df-le2 131
This theorem is referenced by:  ud3lem3  576
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