Theorem ssrabi

Description: Inference of restricted abstraction subclass from implication. (Contributed by Peter Mazsa, 26-Oct-2022)

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

Proof

Step	Hyp	Ref	Expression
1		ssrabi.1	$$⊢\phi \to \psi$$
2	1	a1i	$$⊢x\in A\to \left(\phi \to \psi \right)$$
3	2	ss2rabi	$$⊢\left\{x\in A|\phi \right\}\subseteq \left\{x\in A|\psi \right\}$$