Theorem e00an 42389

Description: Elimination rule identical to mp2an 689. The non-virtual deduction form is the virtual deduction form, which is mp2an 689. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e00an.1	⊢ 𝜑
e00an.2	⊢ 𝜓
e00an.3	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Assertion

Ref	Expression
e00an	⊢ 𝜒

Proof of Theorem e00an

Step	Hyp	Ref	Expression
1		e00an.1	. 2 ⊢ 𝜑
2		e00an.2	. 2 ⊢ 𝜓
3		e00an.3	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
4	1, 2, 3	mp2an 689	1 ⊢ 𝜒

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)