Theorem ee13an 44748

Description: e13an 44747 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee13an.1	⊢ (𝜑 → 𝜓)
ee13an.2	⊢ (𝜑 → (𝜒 → (𝜃 → 𝜏)))
ee13an.3	⊢ ((𝜓 ∧ 𝜏) → 𝜂)

Assertion

Ref	Expression
ee13an	⊢ (𝜑 → (𝜒 → (𝜃 → 𝜂)))

Proof of Theorem ee13an

Step	Hyp	Ref	Expression
1		ee13an.1	. 2 ⊢ (𝜑 → 𝜓)
2		ee13an.2	. 2 ⊢ (𝜑 → (𝜒 → (𝜃 → 𝜏)))
3		ee13an.3	. . 3 ⊢ ((𝜓 ∧ 𝜏) → 𝜂)
4	3	ex 412	. 2 ⊢ (𝜓 → (𝜏 → 𝜂))
5	1, 2, 4	ee13 44502	1 ⊢ (𝜑 → (𝜒 → (𝜃 → 𝜂)))

Syntax hints:   → wi 4   ∧ wa 395

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 207  df-an 396

This theorem is referenced by: (None)