Theorem ee112 42164

Description: e112 42163 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee112.1	⊢ (𝜑 → 𝜓)
ee112.2	⊢ (𝜑 → 𝜒)
ee112.3	⊢ (𝜑 → (𝜃 → 𝜏))
ee112.4	⊢ (𝜓 → (𝜒 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
ee112	⊢ (𝜑 → (𝜃 → 𝜂))

Proof of Theorem ee112

Step	Hyp	Ref	Expression
1		ee112.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	a1d 25	. 2 ⊢ (𝜑 → (𝜃 → 𝜓))
3		ee112.2	. . 3 ⊢ (𝜑 → 𝜒)
4	3	a1d 25	. 2 ⊢ (𝜑 → (𝜃 → 𝜒))
5		ee112.3	. 2 ⊢ (𝜑 → (𝜃 → 𝜏))
6		ee112.4	. 2 ⊢ (𝜓 → (𝜒 → (𝜏 → 𝜂)))
7	2, 4, 5, 6	ee222 42011	1 ⊢ (𝜑 → (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)