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Theorem ud4lem0a 262
Description: Introduce ->4 to the left.
Hypothesis
Ref Expression
ud4lem0a.1 a = b
Assertion
Ref Expression
ud4lem0a (c ->4 a) = (c ->4 b)
Proof of Theorem ud4lem0a
StepHypRef Expression
1 ud4lem0a.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))
51lor 70 . . . 4 (c' v a) = (c' v b)
61ax-r4 37 . . . 4 a' = b'
75, 62an 79 . . 3 ((c' v a) ^ a') = ((c' v b) ^ b')
84, 72or 72 . 2 (((c ^ a) v (c' ^ a)) v ((c' v a) ^ a')) = (((c ^ b) v (c' ^ b)) v ((c' v b) ^ b'))
9 df-i4 47 . 2 (c ->4 a) = (((c ^ a) v (c' ^ a)) v ((c' v a) ^ a'))
10 df-i4 47 . 2 (c ->4 b) = (((c ^ b) v (c' ^ b)) v ((c' v b) ^ b'))
118, 9, 103tr1 63 1 (c ->4 a) = (c ->4 b)
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  nom43  328  ud4  598
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