Theorem rabssab 3289

Description: A restricted class is a subclass of the corresponding unrestricted class. (Contributed by Mario Carneiro, 23-Dec-2016.)

Assertion

Ref	Expression
rabssab	|- { x e. A | ph } C_ { x | ph }

Proof of Theorem rabssab

Step	Hyp	Ref	Expression
1		df-rab 2495	. 2 |- { x e. A | ph } = { x | ( x e. A /\ ph ) }
2		simpr 110	. . 3 |- ( ( x e. A /\ ph ) -> ph )
3	2	ss2abi 3273	. 2 |- { x | ( x e. A /\ ph ) } C_ { x | ph }
4	1, 3	eqsstri 3233	1 |- { x e. A | ph } C_ { x | ph }

Syntax hints:   /\ wa 104   e. wcel 2178   {cab 2193   {crab 2490   C_ wss 3174

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-rab 2495  df-in 3180  df-ss 3187

This theorem is referenced by:  epse  4407  riotasbc  5938  genipv  7657  toponsspwpwg  14609  dmtopon  14610