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Metamath Proof Explorer

Theorem mp2an

Description: An inference based on modus ponens. (Contributed by NM, 13-Apr-1995)

Ref Expression
Hypotheses mp2an.1 ⊢ φ
mp2an.2 ⊢ ψ
mp2an.3 ⊢ φ ∧ ψ → χ
Assertion mp2an ⊢ χ

Proof

Step Hyp Ref Expression
1 mp2an.1 ⊢ φ
2 mp2an.2 ⊢ ψ
3 mp2an.3 ⊢ φ ∧ ψ → χ
4 1 3 mpan ⊢ ψ → χ
5 2 4 ax-mp ⊢ χ