Theorem eel00cT 42279

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

Hypotheses

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

Assertion

Ref	Expression
eel00cT	⊢ (⊤ → 𝜒)

Proof of Theorem eel00cT

Step	Hyp	Ref	Expression
1		eel00cT.2	. . 3 ⊢ 𝜓
2		eel00cT.1	. . . 4 ⊢ 𝜑
3		eel00cT.3	. . . 4 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
4	2, 3	mpan 686	. . 3 ⊢ (𝜓 → 𝜒)
5	1, 4	ax-mp 5	. 2 ⊢ 𝜒
6	5	a1i 11	1 ⊢ (⊤ → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395  ⊤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

This theorem is referenced by: (None)