Theorem e02an 42325

Description: Conjunction form of e02 42324. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e02an.1	⊢ 𝜑
e02an.2	⊢ (   𝜓   ,   𝜒   ▶   𝜃   )
e02an.3	⊢ ((𝜑 ∧ 𝜃) → 𝜏)

Assertion

Ref	Expression
e02an	⊢ (   𝜓   ,   𝜒   ▶   𝜏   )

Proof of Theorem e02an

Step	Hyp	Ref	Expression
1		e02an.1	. 2 ⊢ 𝜑
2		e02an.2	. 2 ⊢ (   𝜓   ,   𝜒   ▶   𝜃   )
3		e02an.3	. . 3 ⊢ ((𝜑 ∧ 𝜃) → 𝜏)
4	3	ex 413	. 2 ⊢ (𝜑 → (𝜃 → 𝜏))
5	1, 2, 4	e02 42324	1 ⊢ (   𝜓   ,   𝜒   ▶   𝜏   )

Syntax hints:   → wi 4   ∧ wa 396  (   wvd2 42204

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  df-vd2 42205

This theorem is referenced by: (None)