Metamath Proof Explorer

Theorem adantlrl

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	adantlrl	$⊢ ((φ \land (τ \land ψ)) \land χ) \to θ$

Step	Hyp	Ref	Expression
1		adantl2.1	$⊢ ((φ \land ψ) \land χ) \to θ$
2		simpr	$⊢ (τ \land ψ) \to ψ$
3	2 1	sylanl2	$⊢ ((φ \land (τ \land ψ)) \land χ) \to θ$