Theorem ee101 45429

Description: e101 45428 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee101.1	⊢ (𝜑 → 𝜓)
ee101.2	⊢ 𝜒
ee101.3	⊢ (𝜑 → 𝜃)
ee101.4	⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏)))

Assertion

Ref	Expression
ee101	⊢ (𝜑 → 𝜏)

Proof of Theorem ee101

Step	Hyp	Ref	Expression
1		ee101.1	. 2 ⊢ (𝜑 → 𝜓)
2		ee101.2	. . 3 ⊢ 𝜒
3	2	a1i 11	. 2 ⊢ (𝜑 → 𝜒)
4		ee101.3	. 2 ⊢ (𝜑 → 𝜃)
5		ee101.4	. 2 ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏)))
6	1, 3, 4, 5	syl3c 67	1 ⊢ (𝜑 → 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)