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Theorem syl3anl3 1220
Description: A syllogism inference. (Contributed by NM, 24-Feb-2005.)
Hypotheses
Ref Expression
syl3anl3.1 (𝜑𝜃)
syl3anl3.2 (((𝜓𝜒𝜃) ∧ 𝜏) → 𝜂)
Assertion
Ref Expression
syl3anl3 (((𝜓𝜒𝜑) ∧ 𝜏) → 𝜂)

Proof of Theorem syl3anl3
StepHypRef Expression
1 syl3anl3.1 . . 3 (𝜑𝜃)
213anim3i 1127 . 2 ((𝜓𝜒𝜑) → (𝜓𝜒𝜃))
3 syl3anl3.2 . 2 (((𝜓𝜒𝜃) ∧ 𝜏) → 𝜂)
42, 3sylan 277 1 (((𝜓𝜒𝜑) ∧ 𝜏) → 𝜂)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by: (None)
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