Metamath Proof Explorer

Theorem adantlll

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004) (Proof shortened by Wolf Lammen, 2-Dec-2012)

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

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