This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 3adant1r

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006) (Proof shortened by Wolf Lammen, 23-Jun-2022)

		Ref	Expression
	Hypothesis	ad4ant3.1	$⊢ (φ \land ψ \land χ) \to θ$
	Assertion	3adant1r	$⊢ ((φ \land τ) \land ψ \land χ) \to θ$

Step	Hyp	Ref	Expression
1		ad4ant3.1	$⊢ (φ \land ψ \land χ) \to θ$
2		simpl	$⊢ (φ \land τ) \to φ$
3	2 1	syl3an1	$⊢ ((φ \land τ) \land ψ \land χ) \to θ$