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Theorem eqeqan12rd 2369
 Description: A useful inference for substituting definitions into an equality. (Contributed by NM, 9-Aug-1994.)
Hypotheses
Ref Expression
eqeqan12rd.1 (φA = B)
eqeqan12rd.2 (ψC = D)
Assertion
Ref Expression
eqeqan12rd ((ψ φ) → (A = CB = D))

Proof of Theorem eqeqan12rd
StepHypRef Expression
1 eqeqan12rd.1 . . 3 (φA = B)
2 eqeqan12rd.2 . . 3 (ψC = D)
31, 2eqeqan12d 2368 . 2 ((φ ψ) → (A = CB = D))
43ancoms 439 1 ((ψ φ) → (A = CB = D))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358   = wceq 1642 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 This theorem is referenced by: (None)
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