Metamath Proof Explorer

Theorem 3adantr1

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005)

		Ref	Expression
	Hypothesis	3adantr.1	$⊢ (φ \land (ψ \land χ)) \to θ$
	Assertion	3adantr1	$⊢ (φ \land (τ \land ψ \land χ)) \to θ$

Step	Hyp	Ref	Expression
1		3adantr.1	$⊢ (φ \land (ψ \land χ)) \to θ$
2		3simpc	$⊢ (τ \land ψ \land χ) \to (ψ \land χ)$
3	2 1	sylan2	$⊢ (φ \land (τ \land ψ \land χ)) \to θ$