Theorem e03an 45483

Description: Conjunction form of e03 45481. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e03an.1	⊢ 𝜑
e03an.2	⊢ (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜏   )
e03an.3	⊢ ((𝜑 ∧ 𝜏) → 𝜂)

Assertion

Ref	Expression
e03an	⊢ (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜂   )

Proof of Theorem e03an

Step	Hyp	Ref	Expression
1		e03an.1	. 2 ⊢ 𝜑
2		e03an.2	. 2 ⊢ (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜏   )
3		e03an.3	. . 3 ⊢ ((𝜑 ∧ 𝜏) → 𝜂)
4	3	ex 418	. 2 ⊢ (𝜑 → (𝜏 → 𝜂))
5	1, 2, 4	e03 45481	1 ⊢ (   𝜓   ,   𝜒   ,   𝜃   ▶   𝜂   )

This proof depends on syntax axioms:   → wi 4   ∧ wa 401  (   wvd3 45329

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  df-3an 1105  df-vd3 45332

This theorem is used by: (None)