Theorem ssab2 3686

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 473	. 2 |- ( ( x e. A /\ ph ) -> x e. A )
2	1	abssi 3677	1 |- { x | ( x e. A /\ ph ) } C_ A

Syntax hints:   /\ wa 384   e. wcel 1990   {cab 2608   C_ wss 3574

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-in 3581  df-ss 3588

This theorem is referenced by:  ssrab2  3687  zfausab  4811  exss  4931  dmopabss  5336  fabexg  7122  isf32lem9  9183  psubspset  35030  psubclsetN  35222