Theorem ee011 45623

Description: e011 45622 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee011.1	⊢ 𝜑
ee011.2	⊢ (𝜓 → 𝜒)
ee011.3	⊢ (𝜓 → 𝜃)
ee011.4	⊢ (𝜑 → (𝜒 → (𝜃 → 𝜏)))

Assertion

Ref	Expression
ee011	⊢ (𝜓 → 𝜏)

Proof of Theorem ee011

Step	Hyp	Ref	Expression
1		ee011.1	. . 3 ⊢ 𝜑
2	1	a1i 11	. 2 ⊢ (𝜓 → 𝜑)
3		ee011.2	. 2 ⊢ (𝜓 → 𝜒)
4		ee011.3	. 2 ⊢ (𝜓 → 𝜃)
5		ee011.4	. 2 ⊢ (𝜑 → (𝜒 → (𝜃 → 𝜏)))
6	2, 3, 4, 5	syl3c 67	1 ⊢ (𝜓 → 𝜏)

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by: (None)