Theorem ee212 45635

Description: e212 45634 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee212.1	⊢ (𝜑 → (𝜓 → 𝜒))
ee212.2	⊢ (𝜑 → 𝜃)
ee212.3	⊢ (𝜑 → (𝜓 → 𝜏))
ee212.4	⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
ee212	⊢ (𝜑 → (𝜓 → 𝜂))

Proof of Theorem ee212

Step	Hyp	Ref	Expression
1		ee212.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		ee212.2	. . 3 ⊢ (𝜑 → 𝜃)
3	2	a1d 26	. 2 ⊢ (𝜑 → (𝜓 → 𝜃))
4		ee212.3	. 2 ⊢ (𝜑 → (𝜓 → 𝜏))
5		ee212.4	. 2 ⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂)))
6	1, 3, 4, 5	ee222 45485	1 ⊢ (𝜑 → (𝜓 → 𝜂))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by: (None)