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Theorem sylan9bbr 436
Description: Nested syllogism inference conjoining dissimilar antecedents. (Contributed by NM, 4-Mar-1995.)
Hypotheses
Ref Expression
sylan9bbr.1 (φ → (ψχ))
sylan9bbr.2 (θ → (χτ))
Assertion
Ref Expression
sylan9bbr ((θ φ) → (ψτ))

Proof of Theorem sylan9bbr
StepHypRef Expression
1 sylan9bbr.1 . . 3 (φ → (ψχ))
2 sylan9bbr.2 . . 3 (θ → (χτ))
31, 2sylan9bb 435 . 2 ((φ θ) → (ψτ))
43ancoms 255 1 ((θ φ) → (ψτ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm5.75  868  mpteq12f  3828  opelopabsb  3988  elreimasng  4634  fvelrnb  5164  fmptco  5273  fconstfvm  5322  f1oiso  5408  mpt2eq123  5506  dfoprab4f  5761  fmpt2x  5768  nnmword  6027  ltmpig  6323  qreccl  8331  0fz1  8659  cbvrald  9242
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