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Theorem sylan9bbr 681
 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 680 . 2 ((φ θ) → (ψτ))
43ancoms 439 1 ((θ φ) → (ψτ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-an 360 This theorem is referenced by:  pm5.75  903  sbcom  2089  sbcom2  2114  2mo  2282  2eu6  2289  elssetkg  4269  fconstfv  5456  f1oiso  5499  mpteq12f  5655  mpt2eq123  5661  fmpt2x  5730  sbth  6206
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