Theorem eel00cT

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

	Ref	Expression
Hypotheses	eel00cT.1	⊢ 𝜑
	eel00cT.2	⊢ 𝜓
	eel00cT.3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
Assertion	eel00cT	⊢ ( ⊤ → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		eel00cT.1	⊢ 𝜑
2		eel00cT.2	⊢ 𝜓
3		eel00cT.3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
4	1 3	mpan	⊢ ( 𝜓 → 𝜒 )
5	2 4	ax-mp	⊢ 𝜒
6	5	a1i	⊢ ( ⊤ → 𝜒 )