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Theorem u1lemnab 650
Description: Lemma for Sasaki implication study. (Contributed by NM, 16-Dec-1997.)
Assertion
Ref Expression
u1lemnab ((a1 b)b) = 0

Proof of Theorem u1lemnab
StepHypRef Expression
1 u1lemonb 635 . . 3 ((a1 b) ∪ b ) = 1
2 oran1 91 . . 3 ((a1 b) ∪ b ) = ((a1 b)b)
3 df-f 42 . . . . 5 0 = 1
43con2 67 . . . 4 0 = 1
54ax-r1 35 . . 3 1 = 0
61, 2, 53tr2 64 . 2 ((a1 b)b) = 0
76con1 66 1 ((a1 b)b) = 0
Colors of variables: term
Syntax hints:   = wb 1   wn 4  wo 6  wa 7  1wt 8  0wf 9  1 wi1 12
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  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:  u1lemn1b  730
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