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Metamath Proof Explorer

Theorem eelT0

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

Ref Expression
Hypotheses eelT0.1 ⊢ ⊤ → φ
eelT0.2 ⊢ ψ
eelT0.3 ⊢ φ ∧ ψ → χ
Assertion eelT0 ⊢ χ

Proof

Step Hyp Ref Expression
1 eelT0.1 ⊢ ⊤ → φ
2 eelT0.2 ⊢ ψ
3 eelT0.3 ⊢ φ ∧ ψ → χ
4 1 3 sylan ⊢ ⊤ ∧ ψ → χ
5 2 4 mpan2 ⊢ ⊤ → χ
6 5 mptru ⊢ χ