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Theorem sylani 398
Description: A syllogism inference. (Contributed by NM, 2-May-1996.)
Hypotheses
Ref Expression
sylani.1 (𝜑𝜒)
sylani.2 (𝜓 → ((𝜒𝜃) → 𝜏))
Assertion
Ref Expression
sylani (𝜓 → ((𝜑𝜃) → 𝜏))

Proof of Theorem sylani
StepHypRef Expression
1 sylani.1 . . 3 (𝜑𝜒)
21a1i 9 . 2 (𝜓 → (𝜑𝜒))
3 sylani.2 . 2 (𝜓 → ((𝜒𝜃) → 𝜏))
42, 3syland 287 1 (𝜓 → ((𝜑𝜃) → 𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
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 is referenced by:  syl2ani  400  lcmdvds  10605
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