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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 ) )

Proof

Step	Hyp	Ref	Expression
1		com12.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		id	⊢ ( 𝜓 → 𝜓 )
3	2 1	syl5com	⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )