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Theorem u3lem1 736
Description: Lemma for unified implication study. (Contributed by NM, 14-Dec-1997.)
Assertion
Ref Expression
u3lem1 ((a3 b) →3 a) = ((ab) ∩ (ab ))

Proof of Theorem u3lem1
StepHypRef Expression
1 comi31 508 . . . 4 a C (a3 b)
21comcom 453 . . 3 (a3 b) C a
32u3lemc4 703 . 2 ((a3 b) →3 a) = ((a3 b)a)
4 u3lemnoa 662 . 2 ((a3 b)a) = ((ab) ∩ (ab ))
53, 4ax-r2 36 1 ((a3 b) →3 a) = ((ab) ∩ (ab ))
Colors of variables: term
Syntax hints:   = wb 1   wn 4  wo 6  wa 7  3 wi3 14
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by:  u3lem1n  741
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