Theorem ee220 42211

Description: e220 42210 without virtual deductions. (Contributed by Alan Sare, 12-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee220.1	⊢ (𝜑 → (𝜓 → 𝜒))
ee220.2	⊢ (𝜑 → (𝜓 → 𝜃))
ee220.3	⊢ 𝜏
ee220.4	⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
ee220	⊢ (𝜑 → (𝜓 → 𝜂))

Proof of Theorem ee220

Step	Hyp	Ref	Expression
1		ee220.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		ee220.2	. 2 ⊢ (𝜑 → (𝜓 → 𝜃))
3		ee220.3	. . 3 ⊢ 𝜏
4	3	2a1i 12	. 2 ⊢ (𝜑 → (𝜓 → 𝜏))
5		ee220.4	. 2 ⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂)))
6	1, 2, 4, 5	ee222 42075	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)