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Theorem sylani 604
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 11 . 2 (𝜓 → (𝜑𝜒))
3 sylani.2 . 2 (𝜓 → ((𝜒𝜃) → 𝜏))
42, 3syland 603 1 (𝜓 → ((𝜑𝜃) → 𝜏))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396
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 206  df-an 397
This theorem is referenced by:  syl2ani  607  inf3lem2  9387  zorn2lem5  10256  uzwo  12651  supxrun  13050  lcmdvds  16313  cramer0  21839  csmdsymi  30696  matunitlindflem2  35774  pmapjoin  37866
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