Metamath Proof Explorer

Theorem adantrlr

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004) (Proof shortened by Wolf Lammen, 4-Dec-2012)

		Ref	Expression
	Hypothesis	adantr2.1	$⊢ (φ \land (ψ \land χ)) \to θ$
	Assertion	adantrlr	$⊢ (φ \land ((ψ \land τ) \land χ)) \to θ$

Step	Hyp	Ref	Expression
1		adantr2.1	$⊢ (φ \land (ψ \land χ)) \to θ$
2		simpl	$⊢ (ψ \land τ) \to ψ$
3	2 1	sylanr1	$⊢ (φ \land ((ψ \land τ) \land χ)) \to θ$