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Theorem ud5lem0b 265
Description: Introduce ->5 to the right.
Hypothesis
Ref Expression
ud5lem0a.1 a = b
Assertion
Ref Expression
ud5lem0b (a ->5 c) = (b ->5 c)
Proof of Theorem ud5lem0b
StepHypRef Expression
1 ud5lem0a.1 . . . . 5 a = b
21ran 78 . . . 4 (a ^ c) = (b ^ c)
31ax-r4 37 . . . . 5 a' = b'
43ran 78 . . . 4 (a' ^ c) = (b' ^ c)
52, 42or 72 . . 3 ((a ^ c) v (a' ^ c)) = ((b ^ c) v (b' ^ c))
63ran 78 . . 3 (a' ^ c') = (b' ^ c')
75, 62or 72 . 2 (((a ^ c) v (a' ^ c)) v (a' ^ c')) = (((b ^ c) v (b' ^ c)) v (b' ^ c'))
8 df-i5 48 . 2 (a ->5 c) = (((a ^ c) v (a' ^ c)) v (a' ^ c'))
9 df-i5 48 . 2 (b ->5 c) = (((b ^ c) v (b' ^ c)) v (b' ^ c'))
107, 8, 93tr1 63 1 (a ->5 c) = (b ->5 c)
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:  ud5  599
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