Theorem ssab2 3267

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 3258	1 |- { x | ( x e. A /\ ph ) } C_ A

Syntax hints:   /\ wa 104   e. wcel 2167   {cab 2182   C_ wss 3157

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 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-in 3163  df-ss 3170

This theorem is referenced by:  ssrab2  3268  zfausab  4175  exss  4260  dmopabss  4878  fabexg  5445