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Metamath Proof Explorer

Theorem adantll

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 4-May-1994) (Proof shortened by Wolf Lammen, 24-Nov-2012)

		Ref	Expression
	Hypothesis	adant2.1	$⊢ (φ \land ψ) \to χ$
	Assertion	adantll	$⊢ ((θ \land φ) \land ψ) \to χ$

Step	Hyp	Ref	Expression
1		adant2.1	$⊢ (φ \land ψ) \to χ$
2		simpr	$⊢ (θ \land φ) \to φ$
3	2 1	sylan	$⊢ ((θ \land φ) \land ψ) \to χ$