Theorem e000 42387

Description: A virtual deduction elimination rule. The non-virtual deduction form of e000 42387 is the virtual deduction form. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e000.1	⊢ 𝜑
e000.2	⊢ 𝜓
e000.3	⊢ 𝜒
e000.4	⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))

Assertion

Ref	Expression
e000	⊢ 𝜃

Proof of Theorem e000

Step	Hyp	Ref	Expression
1		e000.3	. 2 ⊢ 𝜒
2		e000.1	. . 3 ⊢ 𝜑
3		e000.2	. . 3 ⊢ 𝜓
4		e000.4	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
5	2, 3, 4	mp2 9	. 2 ⊢ (𝜒 → 𝜃)
6	1, 5	ax-mp 5	1 ⊢ 𝜃

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5

This theorem is referenced by:  ax6e2ndeqVD  42529