Theorem difsymssdifssd

Description: If the symmetric difference is contained in C , so is one of the differences. (Contributed by AV, 17-Aug-2022)

	Ref	Expression
Hypothesis	difsymssdifssd.1	$$⊢\phi \to \left(A∆B\right)\subseteq C$$
Assertion	difsymssdifssd	$$⊢\phi \to A\setminus B\subseteq C$$

Proof

Step	Hyp	Ref	Expression
1		difsymssdifssd.1	$$⊢\phi \to \left(A∆B\right)\subseteq C$$
2		difsssymdif	$$⊢A\setminus B\subseteq \left(A∆B\right)$$
3	2 1	sstrid	$$⊢\phi \to A\setminus B\subseteq C$$