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Metamath Proof Explorer

Theorem 3adantr2

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	3adantr2	$⊢ (φ \land (ψ \land τ \land χ)) \to θ$

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