Theorem ee210 42169

Description: e210 42168 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee210.1	⊢ (𝜑 → (𝜓 → 𝜒))
ee210.2	⊢ (𝜑 → 𝜃)
ee210.3	⊢ 𝜏
ee210.4	⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
ee210	⊢ (𝜑 → (𝜓 → 𝜂))

Proof of Theorem ee210

Step	Hyp	Ref	Expression
1		ee210.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		ee210.2	. . 3 ⊢ (𝜑 → 𝜃)
3	2	a1d 25	. 2 ⊢ (𝜑 → (𝜓 → 𝜃))
4		ee210.3	. . . 4 ⊢ 𝜏
5	4	a1i 11	. . 3 ⊢ (𝜓 → 𝜏)
6	5	a1i 11	. 2 ⊢ (𝜑 → (𝜓 → 𝜏))
7		ee210.4	. 2 ⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂)))
8	1, 3, 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)