Theorem ee21an 45658

Description: e21an 45657 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee21an.1	⊢ (𝜑 → (𝜓 → 𝜒))
ee21an.2	⊢ (𝜑 → 𝜃)
ee21an.3	⊢ ((𝜒 ∧ 𝜃) → 𝜏)

Assertion

Ref	Expression
ee21an	⊢ (𝜑 → (𝜓 → 𝜏))

Proof of Theorem ee21an

Step	Hyp	Ref	Expression
1		ee21an.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		ee21an.2	. 2 ⊢ (𝜑 → 𝜃)
3		ee21an.3	. . 3 ⊢ ((𝜒 ∧ 𝜃) → 𝜏)
4	3	ex 418	. 2 ⊢ (𝜒 → (𝜃 → 𝜏))
5	1, 2, 4	syl6ci 72	1 ⊢ (𝜑 → (𝜓 → 𝜏))

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)