Theorem ss2rabi

Description: Inference of restricted abstraction subclass from implication. (Contributed by NM, 14-Oct-1999)

	Ref	Expression
Hypothesis	ss2rabi.1	$$⊢x\in A\to \left(\phi \to \psi \right)$$
Assertion	ss2rabi	$$⊢\left\{x\in A|\phi \right\}\subseteq \left\{x\in A|\psi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		ss2rabi.1	$$⊢x\in A\to \left(\phi \to \psi \right)$$
2		ss2rab	$$⊢\left\{x\in A|\phi \right\}\subseteq \left\{x\in A|\psi \right\}\leftrightarrow \forall x\in A\left(\phi \to \psi \right)$$
3	2 1	mprgbir	$$⊢\left\{x\in A|\phi \right\}\subseteq \left\{x\in A|\psi \right\}$$