Theorem eel000cT

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

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

Proof

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