QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  ud5lem0b GIF version

Theorem ud5lem0b 265
Description: Introduce 5 to the right. (Contributed by NM, 23-Nov-1997.)
Hypothesis
Ref Expression
ud5lem0a.1 a = b
Assertion
Ref Expression
ud5lem0b (a5 c) = (b5 c)

Proof of Theorem ud5lem0b
StepHypRef Expression
1 ud5lem0a.1 . . . . 5 a = b
21ran 78 . . . 4 (ac) = (bc)
31ax-r4 37 . . . . 5 a = b
43ran 78 . . . 4 (ac) = (bc)
52, 42or 72 . . 3 ((ac) ∪ (ac)) = ((bc) ∪ (bc))
63ran 78 . . 3 (ac ) = (bc )
75, 62or 72 . 2 (((ac) ∪ (ac)) ∪ (ac )) = (((bc) ∪ (bc)) ∪ (bc ))
8 df-i5 48 . 2 (a5 c) = (((ac) ∪ (ac)) ∪ (ac ))
9 df-i5 48 . 2 (b5 c) = (((bc) ∪ (bc)) ∪ (bc ))
107, 8, 93tr1 63 1 (a5 c) = (b5 c)
Colors of variables: term
Syntax hints:   = wb 1   wn 4  wo 6  wa 7  5 wi5 16
This theorem was proved from axioms:  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i5 48
This theorem is referenced by:  ud5  599
  Copyright terms: Public domain W3C validator