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Theorem ud4lem0b 263
Description: Introduce ->4 to the right.
Hypothesis
Ref Expression
ud4lem0a.1 a = b
Assertion
Ref Expression
ud4lem0b (a ->4 c) = (b ->4 c)
Proof of Theorem ud4lem0b
StepHypRef Expression
1 ud4lem0a.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))
63ax-r5 38 . . . 4 (a' v c) = (b' v c)
76ran 78 . . 3 ((a' v c) ^ c') = ((b' v c) ^ c')
85, 72or 72 . 2 (((a ^ c) v (a' ^ c)) v ((a' v c) ^ c')) = (((b ^ c) v (b' ^ c)) v ((b' v c) ^ c'))
9 df-i4 47 . 2 (a ->4 c) = (((a ^ c) v (a' ^ c)) v ((a' v c) ^ c'))
10 df-i4 47 . 2 (b ->4 c) = (((b ^ c) v (b' ^ c)) v ((b' v c) ^ c'))
118, 9, 103tr1 63 1 (a ->4 c) = (b ->4 c)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->4 wi4 15
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-i4 47
This theorem is referenced by:  i4i3  271  ud4  598
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