Theorem sseq12

Description: Equality theorem for the subclass relationship. (Contributed by NM, 31-May-1999)

	Ref	Expression
Assertion	sseq12	$$⊢\left(A=B\wedge C=D\right)\to \left(A\subseteq C\leftrightarrow B\subseteq D\right)$$

Proof

Step	Hyp	Ref	Expression
1		sseq1	$$⊢A=B\to \left(A\subseteq C\leftrightarrow B\subseteq C\right)$$
2		sseq2	$$⊢C=D\to \left(B\subseteq C\leftrightarrow B\subseteq D\right)$$
3	1 2	sylan9bb	$$⊢\left(A=B\wedge C=D\right)\to \left(A\subseteq C\leftrightarrow B\subseteq D\right)$$