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Theorem sylanr2 403
Description: A syllogism inference. (Contributed by NM, 9-Apr-2005.)
Hypotheses
Ref Expression
sylanr2.1 (𝜑𝜃)
sylanr2.2 ((𝜓 ∧ (𝜒𝜃)) → 𝜏)
Assertion
Ref Expression
sylanr2 ((𝜓 ∧ (𝜒𝜑)) → 𝜏)

Proof of Theorem sylanr2
StepHypRef Expression
1 sylanr2.1 . . 3 (𝜑𝜃)
21anim2i 340 . 2 ((𝜒𝜑) → (𝜒𝜃))
3 sylanr2.2 . 2 ((𝜓 ∧ (𝜒𝜃)) → 𝜏)
42, 3sylan2 284 1 ((𝜓 ∧ (𝜒𝜑)) → 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:  adantrrl  478  adantrrr  479  1stconst  6125  2ndconst  6126  ltexprlemopl  7432  ltexprlemopu  7434  mulsub  8186  fzsubel  9870  expsubap  10371  tgcl  12270
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