Theorem ee22an 42182

Description: e22an 42181 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee22an.1	⊢ (𝜑 → (𝜓 → 𝜒))
ee22an.2	⊢ (𝜑 → (𝜓 → 𝜃))
ee22an.3	⊢ ((𝜒 ∧ 𝜃) → 𝜏)

Assertion

Ref	Expression
ee22an	⊢ (𝜑 → (𝜓 → 𝜏))

Proof of Theorem ee22an

Step	Hyp	Ref	Expression
1		ee22an.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		ee22an.2	. 2 ⊢ (𝜑 → (𝜓 → 𝜃))
3		ee22an.3	. . 3 ⊢ ((𝜒 ∧ 𝜃) → 𝜏)
4	3	ex 412	. 2 ⊢ (𝜒 → (𝜃 → 𝜏))
5	1, 2, 4	syl6c 70	1 ⊢ (𝜑 → (𝜓 → 𝜏))

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 206  df-an 396

This theorem is referenced by: (None)