Theorem ssab2 3277

Description: Subclass relation for the restriction of a class abstraction. (Contributed by NM, 31-Mar-1995.)

Assertion

Ref	Expression
ssab2	|- { x | ( x e. A /\ ph ) } C_ A

Distinct variable group:   x, A

Allowed substitution hint:   ph( x)

Proof of Theorem ssab2

Step	Hyp	Ref	Expression
1		simpl 109	. 2 |- ( ( x e. A /\ ph ) -> x e. A )
2	1	abssi 3268	1 |- { x | ( x e. A /\ ph ) } C_ A

Syntax hints:   /\ wa 104   e. wcel 2176   {cab 2191   C_ wss 3166

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-in 3172  df-ss 3179

This theorem is referenced by:  ssrab2  3278  zfausab  4186  exss  4271  dmopabss  4890  fabexg  5463