Theorem ee02an 42319

Description: e02an 42318 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
ee02an.1	⊢ 𝜑
ee02an.2	⊢ (𝜓 → (𝜒 → 𝜃))
ee02an.3	⊢ ((𝜑 ∧ 𝜃) → 𝜏)

Assertion

Ref	Expression
ee02an	⊢ (𝜓 → (𝜒 → 𝜏))

Proof of Theorem ee02an

Step	Hyp	Ref	Expression
1		ee02an.1	. 2 ⊢ 𝜑
2		ee02an.2	. 2 ⊢ (𝜓 → (𝜒 → 𝜃))
3		ee02an.3	. . 3 ⊢ ((𝜑 ∧ 𝜃) → 𝜏)
4	3	ex 413	. 2 ⊢ (𝜑 → (𝜃 → 𝜏))
5	1, 2, 4	mpsylsyld 69	1 ⊢ (𝜓 → (𝜒 → 𝜏))

Syntax hints:   → wi 4   ∧ wa 396

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 397

This theorem is referenced by: (None)