Metamath Proof Explorer


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