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Theorem mpdi 38
Description: A nested modus ponens deduction. (Contributed by NM, 16-Apr-2005.) (Proof shortened by O'Cat, 15-Jan-2008.)
Hypotheses
Ref Expression
mpdi.1 (ψχ)
mpdi.2 (φ → (ψ → (χθ)))
Assertion
Ref Expression
mpdi (φ → (ψθ))

Proof of Theorem mpdi
StepHypRef Expression
1 mpdi.1 . . 3 (ψχ)
21a1i 10 . 2 (φ → (ψχ))
3 mpdi.2 . 2 (φ → (ψ → (χθ)))
42, 3mpdd 36 1 (φ → (ψθ))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  mpii  39  pm2.43d  44  impt  149  enpw1  6062
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