Theorem mpii 39

Description: A doubly nested modus ponens inference. (Contributed by NM, 31-Dec-1993.) (Proof shortened by Wolf Lammen, 31-Jul-2012.)

Hypotheses

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

Assertion

Ref	Expression
mpii	⊢ (φ → (ψ → θ))

Proof of Theorem mpii

Step	Hyp	Ref	Expression
1		mpii.1	. . 3 ⊢ χ
2	1	a1i 10	. 2 ⊢ (ψ → χ)
3		mpii.2	. 2 ⊢ (φ → (ψ → (χ → θ)))
4	2, 3	mpdi 38	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:  equveli  1988  intmin  3947  dfiin2g  4001