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Theorem ud4lem0b 263
 Description: Introduce →4 to the right.
Hypothesis
Ref Expression
ud4lem0a.1 a = b
Assertion
Ref Expression
ud4lem0b (a4 c) = (b4 c)

Proof of Theorem ud4lem0b
StepHypRef Expression
1 ud4lem0a.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))
63ax-r5 38 . . . 4 (ac) = (bc)
76ran 78 . . 3 ((ac) ∩ c ) = ((bc) ∩ c )
85, 72or 72 . 2 (((ac) ∪ (ac)) ∪ ((ac) ∩ c )) = (((bc) ∪ (bc)) ∪ ((bc) ∩ c ))
9 df-i4 47 . 2 (a4 c) = (((ac) ∪ (ac)) ∪ ((ac) ∩ c ))
10 df-i4 47 . 2 (b4 c) = (((bc) ∪ (bc)) ∪ ((bc) ∩ c ))
118, 9, 103tr1 63 1 (a4 c) = (b4 c)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →4 wi4 15 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-i4 47 This theorem is referenced by:  i4i3  271  ud4  598
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