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Theorem u2lem3 750
 Description: Lemma for unified implication study.
Assertion
Ref Expression
u2lem3 (a2 (b2 a)) = 1

Proof of Theorem u2lem3
StepHypRef Expression
1 df-i2 45 . 2 (a2 (b2 a)) = ((b2 a) ∪ (a ∩ (b2 a) ))
2 u2lemc1 681 . . . . 5 a C (b2 a)
32comcom3 454 . . . 4 a C (b2 a)
42comcom4 455 . . . 4 a C (b2 a)
53, 4fh4 472 . . 3 ((b2 a) ∪ (a ∩ (b2 a) )) = (((b2 a) ∪ a ) ∩ ((b2 a) ∪ (b2 a) ))
6 u2lemonb 636 . . . . 5 ((b2 a) ∪ a ) = 1
7 df-t 41 . . . . . 6 1 = ((b2 a) ∪ (b2 a) )
87ax-r1 35 . . . . 5 ((b2 a) ∪ (b2 a) ) = 1
96, 82an 79 . . . 4 (((b2 a) ∪ a ) ∩ ((b2 a) ∪ (b2 a) )) = (1 ∩ 1)
10 an1 106 . . . 4 (1 ∩ 1) = 1
119, 10ax-r2 36 . . 3 (((b2 a) ∪ a ) ∩ ((b2 a) ∪ (b2 a) )) = 1
125, 11ax-r2 36 . 2 ((b2 a) ∪ (a ∩ (b2 a) )) = 1
131, 12ax-r2 36 1 (a2 (b2 a)) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 8   →2 wi2 13 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-i2 45  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  imp3  841
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