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Theorem u1lemana 605
Description: Lemma for Sasaki implication study.
Assertion
Ref Expression
u1lemana ((a1 b) ∩ a ) = a

Proof of Theorem u1lemana
StepHypRef Expression
1 df-i1 44 . . 3 (a1 b) = (a ∪ (ab))
21ran 78 . 2 ((a1 b) ∩ a ) = ((a ∪ (ab)) ∩ a )
3 ancom 74 . . 3 ((a ∪ (ab)) ∩ a ) = (a ∩ (a ∪ (ab)))
4 anabs 121 . . 3 (a ∩ (a ∪ (ab))) = a
53, 4ax-r2 36 . 2 ((a ∪ (ab)) ∩ a ) = a
62, 5ax-r2 36 1 ((a1 b) ∩ a ) = a
Colors of variables: term
Syntax hints:   = wb 1   wn 4  wo 6  wa 7  1 wi1 12
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i1 44
This theorem is referenced by:  u1lemnoa  660  u12lembi  726  u1lem7  772
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