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Theorem ud5lem0b 265
 Description: Introduce →5 to the right.
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
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