Theorem ee32an 45529

Description: e33an 45503 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee32an.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
ee32an.2	⊢ (𝜑 → (𝜓 → 𝜏))
ee32an.3	⊢ ((𝜃 ∧ 𝜏) → 𝜂)

Assertion

Ref	Expression
ee32an	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂)))

Proof of Theorem ee32an

Step	Hyp	Ref	Expression
1		ee32an.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2		ee32an.2	. . 3 ⊢ (𝜑 → (𝜓 → 𝜏))
3	2	a1dd 51	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜏)))
4		ee32an.3	. 2 ⊢ ((𝜃 ∧ 𝜏) → 𝜂)
5	1, 3, 4	ee33an 45504	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

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)