Theorem ee120 42173

Description: Virtual deduction rule e120 42172 without virtual deduction symbols. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee120.1	⊢ (𝜑 → 𝜓)
ee120.2	⊢ (𝜑 → (𝜒 → 𝜃))
ee120.3	⊢ 𝜏
ee120.4	⊢ (𝜓 → (𝜃 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
ee120	⊢ (𝜑 → (𝜒 → 𝜂))

Proof of Theorem ee120

Step	Hyp	Ref	Expression
1		ee120.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	a1d 25	. 2 ⊢ (𝜑 → (𝜒 → 𝜓))
3		ee120.2	. 2 ⊢ (𝜑 → (𝜒 → 𝜃))
4		ee120.3	. . . 4 ⊢ 𝜏
5	4	a1i 11	. . 3 ⊢ (𝜒 → 𝜏)
6	5	a1i 11	. 2 ⊢ (𝜑 → (𝜒 → 𝜏))
7		ee120.4	. 2 ⊢ (𝜓 → (𝜃 → (𝜏 → 𝜂)))
8	2, 3, 6, 7	ee222 42011	1 ⊢ (𝜑 → (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)