Theorem ss2abiOLD

Description: Obsolete version of ss2abi as of 28-Jun-2024. (Contributed by NM, 31-Mar-1995) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ss2abiOLD.1	$$⊢\phi \to \psi$$
Assertion	ss2abiOLD	$$⊢\left\{x|\phi \right\}\subseteq \left\{x|\psi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		ss2abiOLD.1	$$⊢\phi \to \psi$$
2		ss2ab	$$⊢\left\{x|\phi \right\}\subseteq \left\{x|\psi \right\}\leftrightarrow \forall x\left(\phi \to \psi \right)$$
3	2 1	mpgbir	$$⊢\left\{x|\phi \right\}\subseteq \left\{x|\psi \right\}$$