Theorem mpid 37

Description: A nested modus ponens deduction. (Contributed by NM, 14-Dec-2004.)

Hypotheses

Ref	Expression
mpid.1	⊢ (φ → χ)
mpid.2	⊢ (φ → (ψ → (χ → θ)))

Assertion

Ref	Expression
mpid	⊢ (φ → (ψ → θ))

Proof of Theorem mpid

Step	Hyp	Ref	Expression
1		mpid.1	. . 3 ⊢ (φ → χ)
2	1	a1d 22	. 2 ⊢ (φ → (ψ → χ))
3		mpid.2	. 2 ⊢ (φ → (ψ → (χ → θ)))
4	2, 3	mpdd 36	1 ⊢ (φ → (ψ → θ))

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  2882  rspcimdv  2957  nndisjeq  4430