Theorem e01an 41019

Description: Conjunction form of e01 41018. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e01an.1	⊢ 𝜑
e01an.2	⊢ (   𝜓   ▶   𝜒   )
e01an.3	⊢ ((𝜑 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
e01an	⊢ (   𝜓   ▶   𝜃   )

Proof of Theorem e01an

Step	Hyp	Ref	Expression
1		e01an.1	. 2 ⊢ 𝜑
2		e01an.2	. 2 ⊢ (   𝜓   ▶   𝜒   )
3		e01an.3	. . 3 ⊢ ((𝜑 ∧ 𝜒) → 𝜃)
4	3	ex 415	. 2 ⊢ (𝜑 → (𝜒 → 𝜃))
5	1, 2, 4	e01 41018	1 ⊢ (   𝜓   ▶   𝜃   )

Syntax hints:   → wi 4   ∧ wa 398  (   wvd1 40896

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 209  df-an 399  df-vd1 40897

This theorem is referenced by:  unipwrVD  41159