Theorem psseq1d

Description: An equality deduction for the proper subclass relationship. (Contributed by NM, 9-Jun-2004)

	Ref	Expression
Hypothesis	psseq1d.1	$$⊢\phi \to A=B$$
Assertion	psseq1d	$$⊢\phi \to \left(A\subset C\leftrightarrow B\subset C\right)$$

Proof

Step	Hyp	Ref	Expression
1		psseq1d.1	$$⊢\phi \to A=B$$
2		psseq1	$$⊢A=B\to \left(A\subset C\leftrightarrow B\subset C\right)$$
3	1 2	syl	$$⊢\phi \to \left(A\subset C\leftrightarrow B\subset C\right)$$