Theorem prsspwOLD 4203

Description: An unordered pair belongs to the power class of a class iff each member belongs to the class. (Contributed by NM, 10-Dec-2003.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) Obsolete version of prsspw 4202 as of 25-Mar-2020. (New usage is discouraged.) (Proof modification is discouraged.)

Hypotheses

Ref	Expression
prsspwOLD.1
prsspwOLD.2

Assertion

Ref	Expression
prsspwOLD

Proof of Theorem prsspwOLD

Step	Hyp	Ref	Expression
1		prsspwOLD.1	. . 3
2		prsspwOLD.2	. . 3
3	1, 2	prss 4184	. 2
4	1	elpw 4018	. . 3
5	2	elpw 4018	. . 3
6	4, 5	anbi12i 697	. 2
7	3, 6	bitr3i 251	1

Syntax hints:  <->wb 184  /\wa 369  e.wcel 1818  cvv 3109  C_wss 3475  ~Pcpw 4012  {cpr 4031

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-in 3482  df-ss 3489  df-pw 4014  df-sn 4030  df-pr 4032