Metamath Proof Explorer

Theorem com12

Description: Inference that swaps (commutes) antecedents in an implication. Inference associated with pm2.04 . Its associated inference is mpi . (Contributed by NM, 29-Dec-1992) (Proof shortened by Wolf Lammen, 4-Aug-2012)

Ref Expression
Hypothesis com12.1 φ ψ χ
Assertion com12 ψ φ χ


Step Hyp Ref Expression
1 com12.1 φ ψ χ
2 id ψ ψ
3 2 1 syl5com ψ φ χ