Theorem mp2 17

Description: A double modus ponens inference. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 23-Jul-2013.)

Hypotheses

Ref	Expression
mp2.1	⊢ φ
mp2.2	⊢ ψ
mp2.3	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
mp2	⊢ χ

Proof of Theorem mp2

Step	Hyp	Ref	Expression
1		mp2.1	. 2 ⊢ φ
2		mp2.2	. . 3 ⊢ ψ
3		mp2.3	. . 3 ⊢ (φ → (ψ → χ))
4	2, 3	mpi 16	. 2 ⊢ (φ → χ)
5	1, 4	ax-mp 5	1 ⊢ χ

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  impbii  180  pm3.2i  441  sstri  3282  funopab4  5142  fvsn  5446