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Theorem ud4lem0a 262
 Description: Introduce →4 to the left. (Contributed by NM, 23-Nov-1997.)
Hypothesis
Ref Expression
ud4lem0a.1 a = b
Assertion
Ref Expression
ud4lem0a (c4 a) = (c4 b)

Proof of Theorem ud4lem0a
StepHypRef Expression
1 ud4lem0a.1 . . . . 5 a = b
21lan 77 . . . 4 (ca) = (cb)
31lan 77 . . . 4 (ca) = (cb)
42, 32or 72 . . 3 ((ca) ∪ (ca)) = ((cb) ∪ (cb))
51lor 70 . . . 4 (ca) = (cb)
61ax-r4 37 . . . 4 a = b
75, 62an 79 . . 3 ((ca) ∩ a ) = ((cb) ∩ b )
84, 72or 72 . 2 (((ca) ∪ (ca)) ∪ ((ca) ∩ a )) = (((cb) ∪ (cb)) ∪ ((cb) ∩ b ))
9 df-i4 47 . 2 (c4 a) = (((ca) ∪ (ca)) ∪ ((ca) ∩ a ))
10 df-i4 47 . 2 (c4 b) = (((cb) ∪ (cb)) ∪ ((cb) ∩ b ))
118, 9, 103tr1 63 1 (c4 a) = (c4 b)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ 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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