Theorem spsbbiOLD

Description: Obsolete version of spsbbi as of 6-Jul-2023. Specialization of biconditional. (Contributed by NM, 2-Jun-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	spsbbiOLD	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left(\left[y/x\right]\phi \leftrightarrow \left[y/x\right]\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		stdpc4	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left[y/x\right]\left(\phi \leftrightarrow \psi \right)$$
2		sbbi	$$⊢\left[y/x\right]\left(\phi \leftrightarrow \psi \right)\leftrightarrow \left(\left[y/x\right]\phi \leftrightarrow \left[y/x\right]\psi \right)$$
3	1 2	sylib	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left(\left[y/x\right]\phi \leftrightarrow \left[y/x\right]\psi \right)$$