Theorem syl5imp 42021

Description: Closed form of syl5 34. Derived automatically from syl5impVD 42372. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
syl5imp	⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜃 → 𝜓) → (𝜑 → (𝜃 → 𝜒))))

Proof of Theorem syl5imp

Step	Hyp	Ref	Expression
1		pm2.04 90	. . 3 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))
2	1	imim2d 57	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜃 → 𝜓) → (𝜃 → (𝜑 → 𝜒))))
3	2	com34 91	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜃 → 𝜓) → (𝜑 → (𝜃 → 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: (None)