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Theorem l42modlem2 1148
Description: Lemma for l42mod 1149..
Assertion
Ref Expression
l42modlem2 ((((a v b) ^ c) v d) ^ e) =< (((a v b) v d) ^ ((a v b) v e))
Proof of Theorem l42modlem2
StepHypRef Expression
1 lea 160 . . 3 ((a v b) ^ c) =< (a v b)
21leror 152 . 2 (((a v b) ^ c) v d) =< ((a v b) v d)
3 leor 159 . 2 e =< ((a v b) v e)
42, 3le2an 169 1 ((((a v b) ^ c) v d) ^ e) =< (((a v b) v d) ^ ((a v b) v e))
Colors of variables: term
Syntax hints:   =< wle 2   v wo 6   ^ wa 7
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-t 41  df-f 42  df-le1 130  df-le2 131
This theorem is referenced by:  l42mod  1149
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