Theorem ee002 42153

Description: e002 42152 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee002.1	⊢ 𝜑
ee002.2	⊢ 𝜓
ee002.3	⊢ (𝜒 → (𝜃 → 𝜏))
ee002.4	⊢ (𝜑 → (𝜓 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
ee002	⊢ (𝜒 → (𝜃 → 𝜂))

Proof of Theorem ee002

Step	Hyp	Ref	Expression
1		ee002.1	. . . 4 ⊢ 𝜑
2	1	a1i 11	. . 3 ⊢ (𝜃 → 𝜑)
3	2	a1i 11	. 2 ⊢ (𝜒 → (𝜃 → 𝜑))
4		ee002.2	. . . 4 ⊢ 𝜓
5	4	a1i 11	. . 3 ⊢ (𝜃 → 𝜓)
6	5	a1i 11	. 2 ⊢ (𝜒 → (𝜃 → 𝜓))
7		ee002.3	. 2 ⊢ (𝜒 → (𝜃 → 𝜏))
8		ee002.4	. 2 ⊢ (𝜑 → (𝜓 → (𝜏 → 𝜂)))
9	3, 6, 7, 8	ee222 42011	1 ⊢ (𝜒 → (𝜃 → 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)