Theorem eel000cT 42212

Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
eel000cT.1	⊢ 𝜑
eel000cT.2	⊢ 𝜓
eel000cT.3	⊢ 𝜒
eel000cT.4	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
eel000cT	⊢ (⊤ → 𝜃)

Proof of Theorem eel000cT

Step	Hyp	Ref	Expression
1		eel000cT.3	. . 3 ⊢ 𝜒
2		eel000cT.2	. . . 4 ⊢ 𝜓
3		eel000cT.1	. . . . 5 ⊢ 𝜑
4		eel000cT.4	. . . . 5 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
5	3, 4	mp3an1 1446	. . . 4 ⊢ ((𝜓 ∧ 𝜒) → 𝜃)
6	2, 5	mpan 686	. . 3 ⊢ (𝜒 → 𝜃)
7	1, 6	ax-mp 5	. 2 ⊢ 𝜃
8	7	a1i 11	1 ⊢ (⊤ → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1085  ⊤wtru 1540

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 396  df-3an 1087

This theorem is referenced by: (None)