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Theorem syld3an3 1227
Description: A syllogism inference. (Contributed by NM, 20-May-2007.)
Hypotheses
Ref Expression
syld3an3.1 ((φ ψ χ) → θ)
syld3an3.2 ((φ ψ θ) → τ)
Assertion
Ref Expression
syld3an3 ((φ ψ χ) → τ)

Proof of Theorem syld3an3
StepHypRef Expression
1 simp1 955 . 2 ((φ ψ χ) → φ)
2 simp2 956 . 2 ((φ ψ χ) → ψ)
3 syld3an3.1 . 2 ((φ ψ χ) → θ)
4 syld3an3.2 . 2 ((φ ψ θ) → τ)
51, 2, 3, 4syl3anc 1182 1 ((φ ψ χ) → τ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  syld3an1  1228  syld3an2  1229  resin  5307
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