Metamath Proof Explorer

Theorem ad4ant134

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

		Ref	Expression
	Hypothesis	ad4ant3.1	$⊢ (φ \land ψ \land χ) \to θ$
	Assertion	ad4ant134	$⊢ (((φ \land τ) \land ψ) \land χ) \to θ$

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