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Theorem syl3anl3 1251
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 1154 . 2 ((𝜓𝜒𝜑) → (𝜓𝜒𝜃))
3 syl3anl3.2 . 2 (((𝜓𝜒𝜃) ∧ 𝜏) → 𝜂)
42, 3sylan 281 1 (((𝜓𝜒𝜑) ∧ 𝜏) → 𝜂)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by: (None)
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