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Theorem oa4ctod 968
Description: Derivation of 4-OA law variant.
Hypothesis
Ref Expression
oa4ctod.1 (a' ^ (a v (b ^ (((a ^ b) v ((a ->1 d) ^ (b ->1 d))) v (((a ^ c) v ((a ->1 d) ^ (c ->1 d))) ^ ((b ^ c) v ((b ->1 d) ^ (c ->1 d)))))))) =< d
Assertion
Ref Expression
oa4ctod (b ^ (((a ^ b) v ((a ->1 d) ^ (b ->1 d))) v (((a ^ c) v ((a ->1 d) ^ (c ->1 d))) ^ ((b ^ c) v ((b ->1 d) ^ (c ->1 d)))))) =< (a' ->1 d)
Proof of Theorem oa4ctod
StepHypRef Expression
1 oa4ctod.1 . 2 (a' ^ (a v (b ^ (((a ^ b) v ((a ->1 d) ^ (b ->1 d))) v (((a ^ c) v ((a ->1 d) ^ (c ->1 d))) ^ ((b ^ c) v ((b ->1 d) ^ (c ->1 d)))))))) =< d
21oat 927 1 (b ^ (((a ^ b) v ((a ->1 d) ^ (b ->1 d))) v (((a ^ c) v ((a ->1 d) ^ (c ->1 d))) ^ ((b ^ c) v ((b ->1 d) ^ (c ->1 d)))))) =< (a' ->1 d)
Colors of variables: term
Syntax hints:   =< wle 2  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12
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  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-le1 130  df-le2 131
This theorem is referenced by:  axoa4d  1038
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