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Theorem ud2lem0a 258
Description: Introduce ->2 to the left.
Hypothesis
Ref Expression
ud2lem0a.1 a = b
Assertion
Ref Expression
ud2lem0a (c ->2 a) = (c ->2 b)
Proof of Theorem ud2lem0a
StepHypRef Expression
1 ud2lem0a.1 . . 3 a = b
21ax-r4 37 . . . 4 a' = b'
32lan 77 . . 3 (c' ^ a') = (c' ^ b')
41, 32or 72 . 2 (a v (c' ^ a')) = (b v (c' ^ b'))
5 df-i2 45 . 2 (c ->2 a) = (a v (c' ^ a'))
6 df-i2 45 . 2 (c ->2 b) = (b v (c' ^ b'))
74, 5, 63tr1 63 1 (c ->2 a) = (c ->2 b)
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  i1i2con2  269  nom41  326  ud2  596  3vth6  809  2oath1i1  827  1oath1i1u  828
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