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