Theorem abssi

Description: Inference of abstraction subclass from implication. (Contributed by NM, 20-Jan-2006)

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

Proof

Step	Hyp	Ref	Expression
1		abssi.1	$$⊢\phi \to x\in A$$
2	1	ss2abi	$$⊢\left\{x|\phi \right\}\subseteq \left\{x|x\in A\right\}$$
3		abid2	$$⊢\left\{x|x\in A\right\}=A$$
4	2 3	sseqtri	$$⊢\left\{x|\phi \right\}\subseteq A$$