Theorem cleq1lem

Description: Equality implies bijection. (Contributed by RP, 9-May-2020)

	Ref	Expression
Assertion	cleq1lem	$$⊢A=B\to \left(\left(A\subseteq C\wedge \phi \right)\leftrightarrow \left(B\subseteq C\wedge \phi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		sseq1	$$⊢A=B\to \left(A\subseteq C\leftrightarrow B\subseteq C\right)$$
2	1	anbi1d	$$⊢A=B\to \left(\left(A\subseteq C\wedge \phi \right)\leftrightarrow \left(B\subseteq C\wedge \phi \right)\right)$$