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Theorem u1lemn1b 730
 Description: This theorem continues the line of proofs such as u1lemnaa 640, ud1lem0b 256, u1lemnanb 655, etc. (Contributed by Josiah Burroughs, 26-May-2004.)
Assertion
Ref Expression
u1lemn1b (a1 b) = ((a1 b)1 b)

Proof of Theorem u1lemn1b
StepHypRef Expression
1 ax-a1 30 . . 3 (a1 b) = (a1 b)
2 u1lemnab 650 . . . 4 ((a1 b)b) = 0
32ax-r1 35 . . 3 0 = ((a1 b)b)
41, 32or 72 . 2 ((a1 b) ∪ 0) = ((a1 b) ∪ ((a1 b)b))
5 or0 102 . . 3 ((a1 b) ∪ 0) = (a1 b)
65ax-r1 35 . 2 (a1 b) = ((a1 b) ∪ 0)
7 df-i1 44 . 2 ((a1 b)1 b) = ((a1 b) ∪ ((a1 b)b))
84, 6, 73tr1 63 1 (a1 b) = ((a1 b)1 b)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7  0wf 9   →1 wi1 12 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i1 44 This theorem is referenced by:  u1lem3var1  731  lem4.6.5  1087
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