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Theorem sylanr1 682
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 615 . 2 ((𝜑𝜃) → (𝜒𝜃))
3 sylanr1.2 . 2 ((𝜓 ∧ (𝜒𝜃)) → 𝜏)
42, 3sylan2 593 1 ((𝜓 ∧ (𝜑𝜃)) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 207  df-an 396
This theorem is referenced by:  adantrll  722  adantrlr  723  sbthlem9  9131  unfi  9211  pczpre  16885  cpmadugsumlemF  22882  blsscls2  24517  rpvmasumlem  27531  leopmuli  32152  chirredlem1  32409  chirredlem3  32411  pibt2  37418  mhpind  42604  dvconstbi  44353  bccbc  44364  reccot  49277  rectan  49278  aacllem  49320
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