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Theorem syl3anr1 1171
Description: A syllogism inference. (Contributed by NM, 31-Jul-2007.)
Hypotheses
Ref Expression
syl3anr1.1 (φψ)
syl3anr1.2 ((χ (ψ θ τ)) → η)
Assertion
Ref Expression
syl3anr1 ((χ (φ θ τ)) → η)

Proof of Theorem syl3anr1
StepHypRef Expression
1 syl3anr1.1 . . 3 (φψ)
213anim1i 1075 . 2 ((φ θ τ) → (ψ θ τ))
3 syl3anr1.2 . 2 ((χ (ψ θ τ)) → η)
42, 3sylan2 270 1 ((χ (φ θ τ)) → η)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   w3a 871
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  df-3an 873
This theorem is referenced by: (None)
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