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Theorem sylan2d 292
Description: A syllogism deduction. (Contributed by NM, 15-Dec-2004.)
Hypotheses
Ref Expression
sylan2d.1 (𝜑 → (𝜓𝜒))
sylan2d.2 (𝜑 → ((𝜃𝜒) → 𝜏))
Assertion
Ref Expression
sylan2d (𝜑 → ((𝜃𝜓) → 𝜏))

Proof of Theorem sylan2d
StepHypRef Expression
1 sylan2d.1 . . 3 (𝜑 → (𝜓𝜒))
2 sylan2d.2 . . . 4 (𝜑 → ((𝜃𝜒) → 𝜏))
32ancomsd 267 . . 3 (𝜑 → ((𝜒𝜃) → 𝜏))
41, 3syland 291 . 2 (𝜑 → ((𝜓𝜃) → 𝜏))
54ancomsd 267 1 (𝜑 → ((𝜃𝜓) → 𝜏))
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  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  syl2and  293  sylan2i  405  swopo  4232  prarloclemlo  7322  prodgt02  8631  prodge02  8633
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