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Theorem syl3anl1 1230
Description: A syllogism inference. (Contributed by NM, 24-Feb-2005.)
Hypotheses
Ref Expression
syl3anl1.1 (φψ)
syl3anl1.2 (((ψ χ θ) τ) → η)
Assertion
Ref Expression
syl3anl1 (((φ χ θ) τ) → η)

Proof of Theorem syl3anl1
StepHypRef Expression
1 syl3anl1.1 . . 3 (φψ)
213anim1i 1138 . 2 ((φ χ θ) → (ψ χ θ))
3 syl3anl1.2 . 2 (((ψ χ θ) τ) → η)
42, 3sylan 457 1 (((φ χ θ) τ) → η)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   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: (None)
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