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	|- ( ph -> ( A /_\ B ) C_ C )
Assertion	difsymssdifssd	|- ( ph -> ( A \ B ) C_ C )

Proof

Step	Hyp	Ref	Expression
1		difsymssdifssd.1	|- ( ph -> ( A /_\ B ) C_ C )
2		difsssymdif	|- ( A \ B ) C_ ( A /_\ B )
3	2 1	sstrid	|- ( ph -> ( A \ B ) C_ C )