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Theorem syldan 456
Description: A syllogism deduction with conjoined antecedents. (Contributed by NM, 24-Feb-2005.) (Proof shortened by Wolf Lammen, 6-Apr-2013.)
Hypotheses
Ref Expression
syldan.1 ((φ ψ) → χ)
syldan.2 ((φ χ) → θ)
Assertion
Ref Expression
syldan ((φ ψ) → θ)

Proof of Theorem syldan
StepHypRef Expression
1 syldan.1 . 2 ((φ ψ) → χ)
2 syldan.2 . . . 4 ((φ χ) → θ)
32expcom 424 . . 3 (χ → (φθ))
43adantrd 454 . 2 (χ → ((φ ψ) → θ))
51, 4mpcom 32 1 ((φ ψ) → θ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   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:  sylan2  460  sbcied2  3083  csbied2  3179  lefinaddc  4450  vfinncvntsp  4549  addlec  6208  nchoicelem5  6293
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