Theorem ee03an 42225

Description: Conjunction form of ee03 42223. (Contributed by Alan Sare, 18-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee03an.1	⊢ 𝜑
ee03an.2	⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏)))
ee03an.3	⊢ ((𝜑 ∧ 𝜏) → 𝜂)

Assertion

Ref	Expression
ee03an	⊢ (𝜓 → (𝜒 → (𝜃 → 𝜂)))

Proof of Theorem ee03an

Step	Hyp	Ref	Expression
1		ee03an.1	. 2 ⊢ 𝜑
2		ee03an.2	. 2 ⊢ (𝜓 → (𝜒 → (𝜃 → 𝜏)))
3		ee03an.3	. . 3 ⊢ ((𝜑 ∧ 𝜏) → 𝜂)
4	3	ex 416	. 2 ⊢ (𝜑 → (𝜏 → 𝜂))
5	1, 2, 4	ee03 42223	1 ⊢ (𝜓 → (𝜒 → (𝜃 → 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)