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Theorem syl3anr3 1224
Description: A syllogism inference. (Contributed by NM, 23-Aug-2007.)
Hypotheses
Ref Expression
syl3anr3.1 (𝜑𝜏)
syl3anr3.2 ((𝜒 ∧ (𝜓𝜃𝜏)) → 𝜂)
Assertion
Ref Expression
syl3anr3 ((𝜒 ∧ (𝜓𝜃𝜑)) → 𝜂)

Proof of Theorem syl3anr3
StepHypRef Expression
1 syl3anr3.1 . . 3 (𝜑𝜏)
213anim3i 1127 . 2 ((𝜓𝜃𝜑) → (𝜓𝜃𝜏))
3 syl3anr3.2 . 2 ((𝜒 ∧ (𝜓𝜃𝜏)) → 𝜂)
42, 3sylan2 280 1 ((𝜒 ∧ (𝜓𝜃𝜑)) → 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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