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Metamath Proof Explorer

Theorem an31s

Description: Swap two conjuncts in antecedent. (Contributed by NM, 31-May-2006)

		Ref	Expression
	Hypothesis	an32s.1	$⊢ ((φ \land ψ) \land χ) \to θ$
	Assertion	an31s	$⊢ ((χ \land ψ) \land φ) \to θ$

Step	Hyp	Ref	Expression
1		an32s.1	$⊢ ((φ \land ψ) \land χ) \to θ$
2	1	exp31	$⊢ φ \to (ψ \to (χ \to θ))$
3	2	com13	$⊢ χ \to (ψ \to (φ \to θ))$
4	3	imp31	$⊢ ((χ \land ψ) \land φ) \to θ$