Theorem mp2d 41

Description: A double modus ponens deduction. (Contributed by NM, 23-May-2013.) (Proof shortened by Wolf Lammen, 23-Jul-2013.)

Hypotheses

Ref	Expression
mp2d.1	⊢ (φ → ψ)
mp2d.2	⊢ (φ → χ)
mp2d.3	⊢ (φ → (ψ → (χ → θ)))

Assertion

Ref	Expression
mp2d	⊢ (φ → θ)

Proof of Theorem mp2d

Step	Hyp	Ref	Expression
1		mp2d.1	. 2 ⊢ (φ → ψ)
2		mp2d.2	. . 3 ⊢ (φ → χ)
3		mp2d.3	. . 3 ⊢ (φ → (ψ → (χ → θ)))
4	2, 3	mpid 37	. 2 ⊢ (φ → (ψ → θ))
5	1, 4	mpd 14	1 ⊢ (φ → 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: (None)