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Metamath Proof Explorer

Theorem adantrrr

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

Step	Hyp	Ref	Expression
1		adantr2.1	$⊢ (φ \land (ψ \land χ)) \to θ$
2		simpl	$⊢ (χ \land τ) \to χ$
3	2 1	sylanr2	$⊢ (φ \land (ψ \land (χ \land τ))) \to θ$