This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem mp2ani

Description: An inference based on modus ponens. (Contributed by NM, 12-Dec-2004)

Ref Expression
Hypotheses mp2ani.1 ⊢ ψ
mp2ani.2 ⊢ χ
mp2ani.3 ⊢ φ → ψ ∧ χ → θ
Assertion mp2ani ⊢ φ → θ

Proof

Step Hyp Ref Expression
1 mp2ani.1 ⊢ ψ
2 mp2ani.2 ⊢ χ
3 mp2ani.3 ⊢ φ → ψ ∧ χ → θ
4 1 3 mpani ⊢ φ → χ → θ
5 2 4 mpi ⊢ φ → θ