Metamath Proof Explorer

Theorem ad5ant13

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 14-Apr-2022)

		Ref	Expression
	Hypothesis	ad5ant2.1	$⊢ (φ \land ψ) \to χ$
	Assertion	ad5ant13	$⊢ ((((φ \land θ) \land ψ) \land τ) \land η) \to χ$

Step	Hyp	Ref	Expression
1		ad5ant2.1	$⊢ (φ \land ψ) \to χ$
2	1	adantlr	$⊢ ((φ \land θ) \land ψ) \to χ$
3	2	ad2antrr	$⊢ ((((φ \land θ) \land ψ) \land τ) \land η) \to χ$