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Theorem sylanr2 385
Description: A syllogism inference. (Contributed by NM, 9-Apr-2005.)
Hypotheses
Ref Expression
sylanr2.1 (φθ)
sylanr2.2 ((ψ (χ θ)) → τ)
Assertion
Ref Expression
sylanr2 ((ψ (χ φ)) → τ)

Proof of Theorem sylanr2
StepHypRef Expression
1 sylanr2.1 . . 3 (φθ)
21anim2i 324 . 2 ((χ φ) → (χ θ))
3 sylanr2.2 . 2 ((ψ (χ θ)) → τ)
42, 3sylan2 270 1 ((ψ (χ φ)) → τ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
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 is referenced by:  adantrrl  455  adantrrr  456  1stconst  5754  2ndconst  5755  ltexprlemopl  6425  ltexprlemopu  6427  mulsub  6998
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