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Theorem lem3.3.7i5e2 1073
Description: Equation 3.7 of [PavMeg1999] p. 9. The variable i in the paper is set to 5, and this is the second part of the equation. (Contributed by Roy F. Longton, 3-Jul-05.)
Assertion
Ref Expression
lem3.3.7i5e2 (a ==5 (a ^ b)) = ((a ^ b) ==5 a)
Proof of Theorem lem3.3.7i5e2
StepHypRef Expression
1 ancom 74 . . . 4 ((a ^ b) ^ a) = (a ^ (a ^ b))
2 ancom 74 . . . 4 ((a ^ b)' ^ a') = (a' ^ (a ^ b)')
31, 22or 72 . . 3 (((a ^ b) ^ a) v ((a ^ b)' ^ a')) = ((a ^ (a ^ b)) v (a' ^ (a ^ b)'))
43ax-r1 35 . 2 ((a ^ (a ^ b)) v (a' ^ (a ^ b)')) = (((a ^ b) ^ a) v ((a ^ b)' ^ a'))
5 df-id5 1047 . 2 (a ==5 (a ^ b)) = ((a ^ (a ^ b)) v (a' ^ (a ^ b)'))
6 df-id5 1047 . 2 ((a ^ b) ==5 a) = (((a ^ b) ^ a) v ((a ^ b)' ^ a'))
74, 5, 63tr1 63 1 (a ==5 (a ^ b)) = ((a ^ b) ==5 a)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ==5 wid5 22
This theorem was proved from axioms:  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-id5 1047
This theorem is referenced by: (None)
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