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Theorem ud1lem0b 256
 Description: Introduce →1 to the right. (Contributed by NM, 23-Nov-1997.)
Hypothesis
Ref Expression
ud1lem0a.1 a = b
Assertion
Ref Expression
ud1lem0b (a1 c) = (b1 c)

Proof of Theorem ud1lem0b
StepHypRef Expression
1 ud1lem0a.1 . . . 4 a = b
21ax-r4 37 . . 3 a = b
31ran 78 . . 3 (ac) = (bc)
42, 32or 72 . 2 (a ∪ (ac)) = (b ∪ (bc))
5 df-i1 44 . 2 (a1 c) = (a ∪ (ac))
6 df-i1 44 . 2 (b1 c) = (b ∪ (bc))
74, 5, 63tr1 63 1 (a1 c) = (b1 c)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →1 wi1 12 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-i1 44 This theorem is referenced by:  ud1lem0ab  257  wql1  293  ud1  595  oi3oa3lem1  732  oi3oa3  733  u1lem12  781  1oaiii  823  sac  835  oa4to4u  973  oa4uto4g  975  oa4gto4u  976
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