Theorem ee021 42175

Description: e021 42174 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee021.1	⊢ 𝜑
ee021.2	⊢ (𝜓 → (𝜒 → 𝜃))
ee021.3	⊢ (𝜓 → 𝜏)
ee021.4	⊢ (𝜑 → (𝜃 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
ee021	⊢ (𝜓 → (𝜒 → 𝜂))

Proof of Theorem ee021

Step	Hyp	Ref	Expression
1		ee021.1	. . . 4 ⊢ 𝜑
2	1	a1i 11	. . 3 ⊢ (𝜒 → 𝜑)
3	2	a1i 11	. 2 ⊢ (𝜓 → (𝜒 → 𝜑))
4		ee021.2	. 2 ⊢ (𝜓 → (𝜒 → 𝜃))
5		ee021.3	. . 3 ⊢ (𝜓 → 𝜏)
6	5	a1d 25	. 2 ⊢ (𝜓 → (𝜒 → 𝜏))
7		ee021.4	. 2 ⊢ (𝜑 → (𝜃 → (𝜏 → 𝜂)))
8	3, 4, 6, 7	ee222 42011	1 ⊢ (𝜓 → (𝜒 → 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)