Theorem ee110 42186

Description: e110 42185 without virtual deductions. (Contributed by Alan Sare, 22-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee110.1	⊢ (𝜑 → 𝜓)
ee110.2	⊢ (𝜑 → 𝜒)
ee110.3	⊢ 𝜃
ee110.4	⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏)))

Assertion

Ref	Expression
ee110	⊢ (𝜑 → 𝜏)

Proof of Theorem ee110

Step	Hyp	Ref	Expression
1		ee110.1	. 2 ⊢ (𝜑 → 𝜓)
2		ee110.2	. 2 ⊢ (𝜑 → 𝜒)
3		ee110.3	. . 3 ⊢ 𝜃
4	3	a1i 11	. 2 ⊢ (𝜑 → 𝜃)
5		ee110.4	. 2 ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏)))
6	1, 2, 4, 5	syl3c 66	1 ⊢ (𝜑 → 𝜏)

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)