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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  9130  unfi  9210  pczpre  16881  cpmadugsumlemF  22898  blsscls2  24533  rpvmasumlem  27546  leopmuli  32162  chirredlem1  32419  chirredlem3  32421  pibt2  37400  mhpind  42581  dvconstbi  44330  bccbc  44341  reccot  48989  rectan  48990  aacllem  49032
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