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Theorem negantlem5 853
 Description: Negated antecedent identity. (Contributed by NM, 6-Aug-2001.)
Hypothesis
Ref Expression
negant.1 (a1 c) = (b1 c)
Assertion
Ref Expression
negantlem5 (ac ) = (bc )

Proof of Theorem negantlem5
StepHypRef Expression
1 negant.1 . . 3 (a1 c) = (b1 c)
21ran 78 . 2 ((a1 c) ∩ c ) = ((b1 c) ∩ c )
3 u1lemanb 615 . 2 ((a1 c) ∩ c ) = (ac )
4 u1lemanb 615 . 2 ((b1 c) ∩ c ) = (bc )
52, 3, 43tr2 64 1 (ac ) = (bc )
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∩ wa 7   →1 wi1 12 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-i1 44  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  negantlem6  854  negantlem7  855  negantlem9  859
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