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Metamath Proof Explorer

Theorem mp2

Description: A double modus ponens inference. (Contributed by NM, 5-Apr-1994)

Ref Expression
Hypotheses mp2.1 ⊢ φ
mp2.2 ⊢ ψ
mp2.3 ⊢ φ → ψ → χ
Assertion mp2 ⊢ χ

Proof

Step Hyp Ref Expression
1 mp2.1 ⊢ φ
2 mp2.2 ⊢ ψ
3 mp2.3 ⊢ φ → ψ → χ
4 1 3 ax-mp ⊢ ψ → χ
5 2 4 ax-mp ⊢ χ