Theorem imim12i 59

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 12	. 2 ⊢ ((𝜓 → 𝜒) → (𝜓 → 𝜃))
4	1, 3	syl5 32	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  60  hbim  1559  19.38  1690  cbvexdh  1941  exmoeudc  2108  bj-bdfindis  15593