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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 (a5 (ab)) = ((ab) ≡5 a)

Proof of Theorem lem3.3.7i5e2
StepHypRef Expression
1 ancom 74 . . . 4 ((ab) ∩ a) = (a ∩ (ab))
2 ancom 74 . . . 4 ((ab)a ) = (a ∩ (ab) )
31, 22or 72 . . 3 (((ab) ∩ a) ∪ ((ab)a )) = ((a ∩ (ab)) ∪ (a ∩ (ab) ))
43ax-r1 35 . 2 ((a ∩ (ab)) ∪ (a ∩ (ab) )) = (((ab) ∩ a) ∪ ((ab)a ))
5 df-id5 1047 . 2 (a5 (ab)) = ((a ∩ (ab)) ∪ (a ∩ (ab) ))
6 df-id5 1047 . 2 ((ab) ≡5 a) = (((ab) ∩ a) ∪ ((ab)a ))
74, 5, 63tr1 63 1 (a5 (ab)) = ((ab) ≡5 a)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ 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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