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Theorem syl2and 469
Description: A syllogism deduction. (Contributed by NM, 15-Dec-2004.)
Hypotheses
Ref Expression
syl2and.1 (φ → (ψχ))
syl2and.2 (φ → (θτ))
syl2and.3 (φ → ((χ τ) → η))
Assertion
Ref Expression
syl2and (φ → ((ψ θ) → η))

Proof of Theorem syl2and
StepHypRef Expression
1 syl2and.1 . 2 (φ → (ψχ))
2 syl2and.2 . . 3 (φ → (θτ))
3 syl2and.3 . . 3 (φ → ((χ τ) → η))
42, 3sylan2d 468 . 2 (φ → ((χ θ) → η))
51, 4syland 467 1 (φ → ((ψ θ) → η))
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
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 177  df-an 360
This theorem is referenced by:  anim12d  546  tfin11  4493
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