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Theorem syl2ani 608
 Description: A syllogism inference. (Contributed by NM, 3-Aug-1999.)
Hypotheses
Ref Expression
syl2ani.1 (𝜑𝜒)
syl2ani.2 (𝜂𝜃)
syl2ani.3 (𝜓 → ((𝜒𝜃) → 𝜏))
Assertion
Ref Expression
syl2ani (𝜓 → ((𝜑𝜂) → 𝜏))

Proof of Theorem syl2ani
StepHypRef Expression
1 syl2ani.1 . 2 (𝜑𝜒)
2 syl2ani.2 . . 3 (𝜂𝜃)
3 syl2ani.3 . . 3 (𝜓 → ((𝜒𝜃) → 𝜏))
42, 3sylan2i 607 . 2 (𝜓 → ((𝜒𝜂) → 𝜏))
51, 4sylani 605 1 (𝜓 → ((𝜑𝜂) → 𝜏))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 398 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 209  df-an 399 This theorem is referenced by:  2mo  2732  frxp  7798  mapen  8659  fin1a2lem9  9808  coprmproddvdslem  15984  psss  17803  mgmidmo  17849  aannenlem1  24903  funtransport  33500  cgrxfr  33524  btwnxfr  33525  bj-cbv3tb  34117
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