Theorem ee30an 42229

Description: Conjunction form of ee30 42227. (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 416	. 2 ⊢ (𝜃 → (𝜏 → 𝜂))
5	1, 2, 4	ee30 42227	1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂)))

Syntax hints:   → wi 4   ∧ wa 399

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 210  df-an 400

This theorem is referenced by: (None)