Theorem ee001 41980

Description: e001 41979 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee001.1	⊢ 𝜑
ee001.2	⊢ 𝜓
ee001.3	⊢ (𝜒 → 𝜃)
ee001.4	⊢ (𝜑 → (𝜓 → (𝜃 → 𝜏)))

Assertion

Ref	Expression
ee001	⊢ (𝜒 → 𝜏)

Proof of Theorem ee001

Step	Hyp	Ref	Expression
1		ee001.1	. . 3 ⊢ 𝜑
2	1	a1i 11	. 2 ⊢ (𝜒 → 𝜑)
3		ee001.2	. . 3 ⊢ 𝜓
4	3	a1i 11	. 2 ⊢ (𝜒 → 𝜓)
5		ee001.3	. 2 ⊢ (𝜒 → 𝜃)
6		ee001.4	. 2 ⊢ (𝜑 → (𝜓 → (𝜃 → 𝜏)))
7	2, 4, 5, 6	syl3c 66	1 ⊢ (𝜒 → 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)