Theorem mpdd 36

Description: A nested modus ponens deduction. (Contributed by NM, 12-Dec-2004.)

Hypotheses

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

Assertion

Ref	Expression
mpdd	⊢ (φ → (ψ → θ))

Proof of Theorem mpdd

Step	Hyp	Ref	Expression
1		mpdd.1	. 2 ⊢ (φ → (ψ → χ))
2		mpdd.2	. . 3 ⊢ (φ → (ψ → (χ → θ)))
3	2	a2d 23	. 2 ⊢ (φ → ((ψ → χ) → (ψ → θ)))
4	1, 3	mpd 14	1 ⊢ (φ → (ψ → θ))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  mpid  37  mpdi  38  syld  40  syl6c  60  ax12b  1689  oprabid  5551  enprmaplem3  6079