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Theorem sylan9eqr 2407
 Description: An equality transitivity deduction. (Contributed by NM, 8-May-1994.)
Hypotheses
Ref Expression
sylan9eqr.1 (φA = B)
sylan9eqr.2 (ψB = C)
Assertion
Ref Expression
sylan9eqr ((ψ φ) → A = C)

Proof of Theorem sylan9eqr
StepHypRef Expression
1 sylan9eqr.1 . . 3 (φA = B)
2 sylan9eqr.2 . . 3 (ψB = C)
31, 2sylan9eq 2405 . 2 ((φ ψ) → A = C)
43ancoms 439 1 ((ψ φ) → A = C)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   = wceq 1642 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 This theorem is referenced by:  sbcied2  3083  csbied2  3179  fun2ssres  5145  funssfv  5343  caovmo  5645  fmpt2x  5730  freceq12  6311
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