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Theorem u3lem11a 787
 Description: Lemma for unified implication study. (Contributed by NM, 18-Jan-1998.)
Assertion
Ref Expression
u3lem11a (a3 ((b3 a) →3 (a3 b)) ) = (a3 b )

Proof of Theorem u3lem11a
StepHypRef Expression
1 ud3lem1 570 . . . . 5 ((b3 a) →3 (a3 b)) = (b ∪ (ba ))
2 ancom 74 . . . . . . . 8 (ba ) = (ab )
3 anor3 90 . . . . . . . 8 (ab ) = (ab)
42, 3ax-r2 36 . . . . . . 7 (ba ) = (ab)
54lor 70 . . . . . 6 (b ∪ (ba )) = (b ∪ (ab) )
6 oran1 91 . . . . . 6 (b ∪ (ab) ) = (b ∩ (ab))
75, 6ax-r2 36 . . . . 5 (b ∪ (ba )) = (b ∩ (ab))
81, 7ax-r2 36 . . . 4 ((b3 a) →3 (a3 b)) = (b ∩ (ab))
98con2 67 . . 3 ((b3 a) →3 (a3 b)) = (b ∩ (ab))
109ud3lem0a 260 . 2 (a3 ((b3 a) →3 (a3 b)) ) = (a3 (b ∩ (ab)))
11 u3lem11 786 . 2 (a3 (b ∩ (ab))) = (a3 b )
1210, 11ax-r2 36 1 (a3 ((b3 a) →3 (a3 b)) ) = (a3 b )
 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: (None)
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