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Theorem mpid 37
Description: A nested modus ponens deduction. (Contributed by NM, 14-Dec-2004.)
Hypotheses
Ref Expression
mpid.1 (φχ)
mpid.2 (φ → (ψ → (χθ)))
Assertion
Ref Expression
mpid (φ → (ψθ))

Proof of Theorem mpid
StepHypRef Expression
1 mpid.1 . . 3 (φχ)
21a1d 22 . 2 (φ → (ψχ))
3 mpid.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:  mp2d  41  pm2.43a  45  embantd  50  mtord  641  mpan2d  655  ceqsalt  2881  rspcimdv  2956  nndisjeq  4429
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