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Theorem syland 281
Description: A syllogism deduction. (Contributed by NM, 15-Dec-2004.)
Hypotheses
Ref Expression
syland.1 (𝜑 → (𝜓𝜒))
syland.2 (𝜑 → ((𝜒𝜃) → 𝜏))
Assertion
Ref Expression
syland (𝜑 → ((𝜓𝜃) → 𝜏))

Proof of Theorem syland
StepHypRef Expression
1 syland.1 . . 3 (𝜑 → (𝜓𝜒))
2 syland.2 . . . 4 (𝜑 → ((𝜒𝜃) → 𝜏))
32expd 249 . . 3 (𝜑 → (𝜒 → (𝜃𝜏)))
41, 3syld 44 . 2 (𝜑 → (𝜓 → (𝜃𝜏)))
54impd 246 1 (𝜑 → ((𝜓𝜃) → 𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem is referenced by:  sylan2d  282  syl2and  283  sylani  392  nn0seqcvgd  10263
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