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Theorem ud2lem0b 259
Description: Introduce ->2 to the right.
Hypothesis
Ref Expression
ud2lem0a.1 a = b
Assertion
Ref Expression
ud2lem0b (a ->2 c) = (b ->2 c)
Proof of Theorem ud2lem0b
StepHypRef Expression
1 ud2lem0a.1 . . . . 5 a = b
21ax-r4 37 . . . 4 a' = b'
32ran 78 . . 3 (a' ^ c') = (b' ^ c')
43lor 70 . 2 (c v (a' ^ c')) = (c v (b' ^ c'))
5 df-i2 45 . 2 (a ->2 c) = (c v (a' ^ c'))
6 df-i2 45 . 2 (b ->2 c) = (c v (b' ^ c'))
74, 5, 63tr1 63 1 (a ->2 c) = (b ->2 c)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->2 wi2 13
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-i2 45
This theorem is referenced by:  i2i1  267  i1i2con1  268  ud2  596  2oath1i1  827
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