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Theorem lem3.3.7i0e2 1058
Description: Equation 3.7 of [PavMeg1999] p. 9. The variable i in the paper is set to 0, and this is the second part of the equation. (Contributed by Roy F. Longton, 3-Jul-05.)
Assertion
Ref Expression
lem3.3.7i0e2 (a ==0 (a ^ b)) = ((a ^ b) ==0 a)
Proof of Theorem lem3.3.7i0e2
StepHypRef Expression
1 ancom 74 . 2 ((a' v (a ^ b)) ^ ((a ^ b)' v a)) = (((a ^ b)' v a) ^ (a' v (a ^ b)))
2 df-id0 49 . 2 (a ==0 (a ^ b)) = ((a' v (a ^ b)) ^ ((a ^ b)' v a))
3 df-id0 49 . 2 ((a ^ b) ==0 a) = (((a ^ b)' v a) ^ (a' v (a ^ b)))
41, 2, 33tr1 63 1 (a ==0 (a ^ b)) = ((a ^ b) ==0 a)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ==0 wid0 17
This theorem was proved from axioms:  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37
This theorem depends on definitions:  df-a 40  df-id0 49
This theorem is referenced by: (None)
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