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Metamath Proof Explorer

Theorem mpanr2

Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994) (Proof shortened by Andrew Salmon, 7-May-2011) (Proof shortened by Wolf Lammen, 7-Apr-2013)

	Ref	Expression
Hypotheses	mpanr2.1	$⊢ χ$
	mpanr2.2	$⊢ (φ \land (ψ \land χ)) \to θ$
Assertion	mpanr2	$⊢ (φ \land ψ) \to θ$

Proof

Step	Hyp	Ref	Expression
1		mpanr2.1	$⊢ χ$
2		mpanr2.2	$⊢ (φ \land (ψ \land χ)) \to θ$
3	1	jctr	$⊢ ψ \to (ψ \land χ)$
4	3 2	sylan2	$⊢ (φ \land ψ) \to θ$