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Theorem ud1lem0b 256
Description: Introduce ->1 to the right.
Hypothesis
Ref Expression
ud1lem0a.1 a = b
Assertion
Ref Expression
ud1lem0b (a ->1 c) = (b ->1 c)
Proof of Theorem ud1lem0b
StepHypRef Expression
1 ud1lem0a.1 . . . 4 a = b
21ax-r4 37 . . 3 a' = b'
31ran 78 . . 3 (a ^ c) = (b ^ c)
42, 32or 72 . 2 (a' v (a ^ c)) = (b' v (b ^ c))
5 df-i1 44 . 2 (a ->1 c) = (a' v (a ^ c))
6 df-i1 44 . 2 (b ->1 c) = (b' v (b ^ c))
74, 5, 63tr1 63 1 (a ->1 c) = (b ->1 c)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v 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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