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Theorem sylan9r 407
Description: Nested syllogism inference conjoining dissimilar antecedents. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
sylan9r.1 (𝜑 → (𝜓𝜒))
sylan9r.2 (𝜃 → (𝜒𝜏))
Assertion
Ref Expression
sylan9r ((𝜃𝜑) → (𝜓𝜏))

Proof of Theorem sylan9r
StepHypRef Expression
1 sylan9r.1 . . 3 (𝜑 → (𝜓𝜒))
2 sylan9r.2 . . 3 (𝜃 → (𝜒𝜏))
31, 2syl9r 73 . 2 (𝜃 → (𝜑 → (𝜓𝜏)))
43imp 123 1 ((𝜃𝜑) → (𝜓𝜏))
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
This theorem is referenced by:  spimt  1714  sbequi  1811  updjudhf  6964  genpcdl  7339  genpcuu  7340  iccsupr  9761  climuni  11074  tgcn  12391  metrest  12689
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