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Metamath Proof Explorer

Theorem 3adantl1

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005)

		Ref	Expression
	Hypothesis	3adantl.1	$⊢ ((φ \land ψ) \land χ) \to θ$
	Assertion	3adantl1	$⊢ ((τ \land φ \land ψ) \land χ) \to θ$

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