Theorem ssab2 3332

Description: Subclass relation for the restriction of a class abstraction. Prefer using the more natural statement ssrab2 3333. (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 3323	1 |- { x | ( x e. A /\ ph ) } C_ A

This proof depends on syntax axioms:   /\ wa 104   e. wcel 2209   {cab 2224   C_ wss 3220

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-in 3226  df-ss 3233

This theorem is used by:  ssrab2  3333  sepab  4278  exss  4367  dmopabss  4993  fabexg  5579