Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  negantlem6 GIF version

Theorem negantlem6 854
 Description: Negated antecedent identity. (Contributed by NM, 6-Aug-2001.)
Hypothesis
Ref Expression
negant.1 (a1 c) = (b1 c)
Assertion
Ref Expression
negantlem6 (ac ) = (bc )

Proof of Theorem negantlem6
StepHypRef Expression
1 negant.1 . . . 4 (a1 c) = (b1 c)
21negant 852 . . 3 (a1 c) = (b1 c)
32negantlem5 853 . 2 (a c ) = (b c )
4 ax-a1 30 . . 3 a = a
54ran 78 . 2 (ac ) = (a c )
6 ax-a1 30 . . 3 b = b
76ran 78 . 2 (bc ) = (b c )
83, 5, 73tr1 63 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:  negantlem8  856  negant2  858
 Copyright terms: Public domain W3C validator