Theorem ee30an 45728

Description: Conjunction form of ee30 45726. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee30an.1	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
ee30an.2	⊢ 𝜏
ee30an.3	⊢ ((𝜃 ∧ 𝜏) → 𝜂)

Assertion

Ref	Expression
ee30an	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂)))

Proof of Theorem ee30an

Step	Hyp	Ref	Expression
1		ee30an.1	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
2		ee30an.2	. 2 ⊢ 𝜏
3		ee30an.3	. . 3 ⊢ ((𝜃 ∧ 𝜏) → 𝜂)
4	3	ex 418	. 2 ⊢ (𝜃 → (𝜏 → 𝜂))
5	1, 2, 4	ee30 45726	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)