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Metamath Proof Explorer

Theorem eelTT

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

Ref Expression
Hypotheses eelTT.1 ⊢ ⊤ → φ
eelTT.2 ⊢ ⊤ → ψ
eelTT.3 ⊢ φ ∧ ψ → χ
Assertion eelTT ⊢ χ

Proof

Step Hyp Ref Expression
1 eelTT.1 ⊢ ⊤ → φ
2 eelTT.2 ⊢ ⊤ → ψ
3 eelTT.3 ⊢ φ ∧ ψ → χ
4 truan ⊢ ⊤ ∧ ψ ↔ ψ
5 1 3 sylan ⊢ ⊤ ∧ ψ → χ
6 4 5 sylbir ⊢ ψ → χ
7 2 6 syl ⊢ ⊤ → χ
8 7 mptru ⊢ χ