Theorem ee202 45623

Description: e202 45622 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee202.1	⊢ (𝜑 → (𝜓 → 𝜒))
ee202.2	⊢ 𝜃
ee202.3	⊢ (𝜑 → (𝜓 → 𝜏))
ee202.4	⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂)))

Assertion

Ref	Expression
ee202	⊢ (𝜑 → (𝜓 → 𝜂))

Proof of Theorem ee202

Step	Hyp	Ref	Expression
1		ee202.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		ee202.2	. . . 4 ⊢ 𝜃
3	2	a1i 11	. . 3 ⊢ (𝜓 → 𝜃)
4	3	a1i 11	. 2 ⊢ (𝜑 → (𝜓 → 𝜃))
5		ee202.3	. 2 ⊢ (𝜑 → (𝜓 → 𝜏))
6		ee202.4	. 2 ⊢ (𝜒 → (𝜃 → (𝜏 → 𝜂)))
7	1, 4, 5, 6	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)