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	⊢ (ψ → χ)
mpdi.2	⊢ (φ → (ψ → (χ → θ)))

Assertion

Ref	Expression
mpdi	⊢ (φ → (ψ → θ))

Proof of Theorem mpdi

Step	Hyp	Ref	Expression
1		mpdi.1	. . 3 ⊢ (ψ → χ)
2	1	a1i 10	. 2 ⊢ (φ → (ψ → χ))
3		mpdi.2	. 2 ⊢ (φ → (ψ → (χ → θ)))
4	2, 3	mpdd 36	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:  mpii  39  pm2.43d  44  impt  149  enpw1  6063