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Theorem sylan9bbr 451
Description: Nested syllogism inference conjoining dissimilar antecedents. (Contributed by NM, 4-Mar-1995.)
Hypotheses
Ref Expression
sylan9bbr.1 (𝜑 → (𝜓𝜒))
sylan9bbr.2 (𝜃 → (𝜒𝜏))
Assertion
Ref Expression
sylan9bbr ((𝜃𝜑) → (𝜓𝜏))

Proof of Theorem sylan9bbr
StepHypRef Expression
1 sylan9bbr.1 . . 3 (𝜑 → (𝜓𝜒))
2 sylan9bbr.2 . . 3 (𝜃 → (𝜒𝜏))
31, 2sylan9bb 450 . 2 ((𝜑𝜃) → (𝜓𝜏))
43ancoms 264 1 ((𝜃𝜑) → (𝜓𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103
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
This theorem is referenced by:  pm5.75  904  mpteq12f  3884  opelopabsb  4051  elreimasng  4753  fvelrnb  5297  fmptco  5406  fconstfvm  5455  f1oiso  5544  mpt2eq123  5643  dfoprab4f  5898  fmpt2x  5905  nnmword  6207  ltmpig  6801  qreccl  9022  0fz1  9354  zmodid2  9648  divgcdcoprm0  10863  cbvrald  11031
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