Theorem ee201 42171

Description: e201 42170 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee201.1	⊢ (𝜑 → (𝜓 → 𝜒))
ee201.2	⊢ 𝜃
ee201.3	⊢ (𝜑 → 𝜏)
ee201.4	⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
ee201	⊢ (𝜑 → (𝜓 → 𝜂))

Proof of Theorem ee201

Step	Hyp	Ref	Expression
1		ee201.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		ee201.2	. . . 4 ⊢ 𝜃
3	2	a1i 11	. . 3 ⊢ (𝜓 → 𝜃)
4	3	a1i 11	. 2 ⊢ (𝜑 → (𝜓 → 𝜃))
5		ee201.3	. . 3 ⊢ (𝜑 → 𝜏)
6	5	a1d 25	. 2 ⊢ (𝜑 → (𝜓 → 𝜏))
7		ee201.4	. 2 ⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂)))
8	1, 4, 6, 7	ee222 42011	1 ⊢ (𝜑 → (𝜓 → 𝜂))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396

This theorem is referenced by: (None)