Theorem ssab2 2133

Description: Subclass relation for the restriction of a class abstraction.

Assertion

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

Distinct variable group:   x,A

Proof of Theorem ssab2

Step	Hyp	Ref	Expression
1		pm3.26 319	. 2 |- ((x e. A /\ ph) -> x e. A)
2	1	abssi 2125	1 |- {x | (x e. A /\ ph)} (_ A

Syntax hints:   /\ wa 223   e. wcel 960  {cab 1466   (_ wss 2050

This theorem is referenced by:  ssrab2 2134  zfausab 2728  exss 2775  onminex 3026  dmopabss 3327  fabexg 3659  sumex 6981  chsssh 9089  qusp 10541

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-in 2054  df-ss 2056

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