Metamath Proof Explorer

Theorem ad5ant125

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 23-Jun-2022) (Proof shortened by Garrett Katz, 13-Jun-2026)

		Ref	Expression
	Hypothesis	ad5ant.1	$⊢ (φ \land ψ \land χ) \to θ$
	Assertion	ad5ant125	$⊢ ((((φ \land ψ) \land τ) \land η) \land χ) \to θ$

Proof

Step	Hyp	Ref	Expression
1		ad5ant.1	$⊢ (φ \land ψ \land χ) \to θ$
2	1	3expa	$⊢ ((φ \land ψ) \land χ) \to θ$
3	2	ad4ant14	$⊢ ((((φ \land ψ) \land τ) \land η) \land χ) \to θ$