Theorem ee010 42312

Description: e010 42311 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee010.1	⊢ 𝜑
ee010.2	⊢ (𝜓 → 𝜒)
ee010.3	⊢ 𝜃
ee010.4	⊢ (𝜑 → (𝜒 → (𝜃 → 𝜏)))

Assertion

Ref	Expression
ee010	⊢ (𝜓 → 𝜏)

Proof of Theorem ee010

Step	Hyp	Ref	Expression
1		ee010.1	. . 3 ⊢ 𝜑
2	1	a1i 11	. 2 ⊢ (𝜓 → 𝜑)
3		ee010.2	. 2 ⊢ (𝜓 → 𝜒)
4		ee010.3	. . 3 ⊢ 𝜃
5	4	a1i 11	. 2 ⊢ (𝜓 → 𝜃)
6		ee010.4	. 2 ⊢ (𝜑 → (𝜒 → (𝜃 → 𝜏)))
7	2, 3, 5, 6	syl3c 66	1 ⊢ (𝜓 → 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)