Theorem cleq2lem

Description: Equality implies bijection. (Contributed by RP, 24-Jul-2020)

	Ref	Expression
Hypothesis	cleq2lem.b	$$⊢A=B\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	cleq2lem	$$⊢A=B\to \left(\left(R\subseteq A\wedge \phi \right)\leftrightarrow \left(R\subseteq B\wedge \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		cleq2lem.b	$$⊢A=B\to \left(\phi \leftrightarrow \psi \right)$$
2		sseq2	$$⊢A=B\to \left(R\subseteq A\leftrightarrow R\subseteq B\right)$$
3	2 1	anbi12d	$$⊢A=B\to \left(\left(R\subseteq A\wedge \phi \right)\leftrightarrow \left(R\subseteq B\wedge \psi \right)\right)$$