Theorem imim12i 53

Description: Inference joining two implications. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 29-Oct-2011.)

Hypotheses

Ref	Expression
imim12i.1	⊢ (φ → ψ)
imim12i.2	⊢ (χ → θ)

Assertion

Ref	Expression
imim12i	⊢ ((ψ → χ) → (φ → θ))

Proof of Theorem imim12i

Step	Hyp	Ref	Expression
1		imim12i.1	. 2 ⊢ (φ → ψ)
2		imim12i.2	. . 3 ⊢ (χ → θ)
3	2	imim2i 13	. 2 ⊢ ((ψ → χ) → (ψ → θ))
4	1, 3	syl5 28	1 ⊢ ((ψ → χ) → (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:  imim1i  54  dedlem0b  919  meredith  1404  19.38OLD  1874  exmoeu  2246