Metamath Proof Explorer

Theorem adantllr

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

		Ref	Expression
	Hypothesis	adantl2.1	$⊢ ((φ \land ψ) \land χ) \to θ$
	Assertion	adantllr	$⊢ (((φ \land τ) \land ψ) \land χ) \to θ$

Step	Hyp	Ref	Expression
1		adantl2.1	$⊢ ((φ \land ψ) \land χ) \to θ$
2		simpl	$⊢ (φ \land τ) \to φ$
3	2 1	sylanl1	$⊢ (((φ \land τ) \land ψ) \land χ) \to θ$