Theorem ee100 42165

Description: e100 42164 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee100.1	⊢ (𝜑 → 𝜓)
ee100.2	⊢ 𝜒
ee100.3	⊢ 𝜃
ee100.4	⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏)))

Assertion

Ref	Expression
ee100	⊢ (𝜑 → 𝜏)

Proof of Theorem ee100

Step	Hyp	Ref	Expression
1		ee100.1	. 2 ⊢ (𝜑 → 𝜓)
2		ee100.2	. . 3 ⊢ 𝜒
3	2	a1i 11	. 2 ⊢ (𝜑 → 𝜒)
4		ee100.3	. . 3 ⊢ 𝜃
5	4	a1i 11	. 2 ⊢ (𝜑 → 𝜃)
6		ee100.4	. 2 ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏)))
7	1, 3, 5, 6	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)