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Theorem ud5lem0a 264
Description: Introduce ->5 to the left.
Hypothesis
Ref Expression
ud5lem0a.1 a = b
Assertion
Ref Expression
ud5lem0a (c ->5 a) = (c ->5 b)
Proof of Theorem ud5lem0a
StepHypRef Expression
1 ud5lem0a.1 . . . . 5 a = b
21lan 77 . . . 4 (c ^ a) = (c ^ b)
31lan 77 . . . 4 (c' ^ a) = (c' ^ b)
42, 32or 72 . . 3 ((c ^ a) v (c' ^ a)) = ((c ^ b) v (c' ^ b))
51ax-r4 37 . . . 4 a' = b'
65lan 77 . . 3 (c' ^ a') = (c' ^ b')
74, 62or 72 . 2 (((c ^ a) v (c' ^ a)) v (c' ^ a')) = (((c ^ b) v (c' ^ b)) v (c' ^ b'))
8 df-i5 48 . 2 (c ->5 a) = (((c ^ a) v (c' ^ a)) v (c' ^ a'))
9 df-i5 48 . 2 (c ->5 b) = (((c ^ b) v (c' ^ b)) v (c' ^ b'))
107, 8, 93tr1 63 1 (c ->5 a) = (c ->5 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->5 wi5 16
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-i5 48
This theorem is referenced by:  nom45  330  ud5  599
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