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	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	com12	$$⊢\psi \to \left(\phi \to \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		com12.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		id	$$⊢\psi \to \psi$$
3	2 1	syl5com	$$⊢\psi \to \left(\phi \to \chi \right)$$