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Theorem i3orlem1 552
Description: Lemma for Kalmbach implication OR builder.
Assertion
Ref Expression
i3orlem1 ((a v c) ^ ((a v c)' v (b v c))) =< ((a v c) ->3 (b v c))
Proof of Theorem i3orlem1
StepHypRef Expression
1 leor 159 . 2 ((a v c) ^ ((a v c)' v (b v c))) =< ((((a v c)' ^ (b v c)) v ((a v c)' ^ (b v c)')) v ((a v c) ^ ((a v c)' v (b v c))))
2 df-i3 46 . . 3 ((a v c) ->3 (b v c)) = ((((a v c)' ^ (b v c)) v ((a v c)' ^ (b v c)')) v ((a v c) ^ ((a v c)' v (b v c))))
32ax-r1 35 . 2 ((((a v c)' ^ (b v c)) v ((a v c)' ^ (b v c)')) v ((a v c) ^ ((a v c)' v (b v c)))) = ((a v c) ->3 (b v c))
41, 3lbtr 139 1 ((a v c) ^ ((a v c)' v (b v c))) =< ((a v c) ->3 (b v c))
Colors of variables: term
Syntax hints:   =< wle 2  'wn 4   v wo 6   ^ wa 7   ->3 wi3 14
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-i3 46  df-le1 130  df-le2 131
This theorem is referenced by:  i3orlem2  553  i3orlem3  554
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