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Theorem neleq12d 2609
 Description: Equality theorem for negated membership. (Contributed by FL, 10-Aug-2016.)
Hypotheses
Ref Expression
neleq12d.1 (φA = B)
neleq12d.2 (φC = D)
Assertion
Ref Expression
neleq12d (φ → (A CB D))

Proof of Theorem neleq12d
StepHypRef Expression
1 neleq12d.1 . . 3 (φA = B)
2 neleq1 2607 . . 3 (A = B → (A CB C))
31, 2syl 15 . 2 (φ → (A CB C))
4 neleq12d.2 . . 3 (φC = D)
5 neleq2 2608 . . 3 (C = D → (B CB D))
64, 5syl 15 . 2 (φ → (B CB D))
73, 6bitrd 244 1 (φ → (A CB D))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642   ∉ wnel 2517 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-clel 2349  df-nel 2519 This theorem is referenced by: (None)
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