Theorem iota2d 5581

Description: A condition that allows us to represent "the unique element such that " with a class expression . (Contributed by NM, 30-Dec-2014.)

Hypotheses

Ref	Expression
iota2df.1
iota2df.2
iota2df.3

Assertion

Ref	Expression
iota2d

Distinct variable groups:   ,   ,   ,

Proof of Theorem iota2d

Step	Hyp	Ref	Expression
1		iota2df.1	. 2
2		iota2df.2	. 2
3		iota2df.3	. 2
4		nfv 1707	. 2
5		nfvd 1708	. 2
6		nfcvd 2620	. 2
7	1, 2, 3, 4, 5, 6	iota2df 5580	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  E!weu 2282  iotacio 5554

This theorem is referenced by:  erov  7427  psgnvalii  16534  q1peqb  22555

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-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-v 3111  df-sbc 3328  df-un 3480  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556