Theorem ss2abdvOLD

Description: Obsolete version of ss2abdv as of 28-Jun-2024. (Contributed by NM, 29-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ss2abdvOLD.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	ss2abdvOLD	$$⊢\phi \to \left\{x|\psi \right\}\subseteq \left\{x|\chi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		ss2abdvOLD.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2	1	alrimiv	$$⊢\phi \to \forall x\left(\psi \to \chi \right)$$
3		ss2ab	$$⊢\left\{x|\psi \right\}\subseteq \left\{x|\chi \right\}\leftrightarrow \forall x\left(\psi \to \chi \right)$$
4	2 3	sylibr	$$⊢\phi \to \left\{x|\psi \right\}\subseteq \left\{x|\chi \right\}$$