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Theorem testmod1 1212
Description: A modular law experiment.
Assertion
Ref Expression
testmod1 (((c v a) v ((b v c) ^ (d v a))) ^ (a v (b ^ (d v ((a v c) ^ (b v d)))))) = (a v (b ^ (((a v c) ^ (b v d)) v (d ^ ((a v c) v ((b v c) ^ (d v a)))))))
Proof of Theorem testmod1
StepHypRef Expression
1 testmod 1211 . 2 (((c v a) v ((b v c) ^ (d v a))) ^ (a v (b ^ (d v ((a v c) ^ (b v d)))))) = ((b ^ ((((a v c) v ((b v c) ^ (d v a))) ^ d) v ((a v c) ^ (b v d)))) v a)
2 orcom 73 . . 3 ((b ^ ((((a v c) v ((b v c) ^ (d v a))) ^ d) v ((a v c) ^ (b v d)))) v a) = (a v (b ^ ((((a v c) v ((b v c) ^ (d v a))) ^ d) v ((a v c) ^ (b v d)))))
3 orcom 73 . . . . . 6 ((((a v c) v ((b v c) ^ (d v a))) ^ d) v ((a v c) ^ (b v d))) = (((a v c) ^ (b v d)) v (((a v c) v ((b v c) ^ (d v a))) ^ d))
4 ancom 74 . . . . . . 7 (((a v c) v ((b v c) ^ (d v a))) ^ d) = (d ^ ((a v c) v ((b v c) ^ (d v a))))
54lor 70 . . . . . 6 (((a v c) ^ (b v d)) v (((a v c) v ((b v c) ^ (d v a))) ^ d)) = (((a v c) ^ (b v d)) v (d ^ ((a v c) v ((b v c) ^ (d v a)))))
63, 5tr 62 . . . . 5 ((((a v c) v ((b v c) ^ (d v a))) ^ d) v ((a v c) ^ (b v d))) = (((a v c) ^ (b v d)) v (d ^ ((a v c) v ((b v c) ^ (d v a)))))
76lan 77 . . . 4 (b ^ ((((a v c) v ((b v c) ^ (d v a))) ^ d) v ((a v c) ^ (b v d)))) = (b ^ (((a v c) ^ (b v d)) v (d ^ ((a v c) v ((b v c) ^ (d v a))))))
87lor 70 . . 3 (a v (b ^ ((((a v c) v ((b v c) ^ (d v a))) ^ d) v ((a v c) ^ (b v d))))) = (a v (b ^ (((a v c) ^ (b v d)) v (d ^ ((a v c) v ((b v c) ^ (d v a)))))))
92, 8tr 62 . 2 ((b ^ ((((a v c) v ((b v c) ^ (d v a))) ^ d) v ((a v c) ^ (b v d)))) v a) = (a v (b ^ (((a v c) ^ (b v d)) v (d ^ ((a v c) v ((b v c) ^ (d v a)))))))
101, 9tr 62 1 (((c v a) v ((b v c) ^ (d v a))) ^ (a v (b ^ (d v ((a v c) ^ (b v d)))))) = (a v (b ^ (((a v c) ^ (b v d)) v (d ^ ((a v c) v ((b v c) ^ (d v a)))))))
Colors of variables: term
Syntax hints:   = wb 1   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  ax-ml 1120
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: (None)
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