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Theorem sylanr1 402
Description: A syllogism inference. (Contributed by NM, 9-Apr-2005.)
Hypotheses
Ref Expression
sylanr1.1 (𝜑𝜒)
sylanr1.2 ((𝜓 ∧ (𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
sylanr1 ((𝜓 ∧ (𝜑𝜃)) → 𝜏)

Proof of Theorem sylanr1
StepHypRef Expression
1 sylanr1.1 . . 3 (𝜑𝜒)
21anim1i 338 . 2 ((𝜑𝜃) → (𝜒𝜃))
3 sylanr1.2 . 2 ((𝜓 ∧ (𝜒𝜃)) → 𝜏)
42, 3sylan2 284 1 ((𝜓 ∧ (𝜑𝜃)) → 𝜏)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103
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 is referenced by:  adantrll  481  adantrlr  482  pczpre  12251  blsscls2  13287
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