Theorem riota2f 6279

Description: This theorem shows a condition that allows us to represent a descriptor with a class expression . (Contributed by NM, 23-Aug-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)

Hypotheses

Ref	Expression
riota2f.1
riota2f.2
riota2f.3

Assertion

Ref	Expression
riota2f

Distinct variable group:   ,

Proof of Theorem riota2f

Step	Hyp	Ref	Expression
1		riota2f.1	. . 3
2	1	nfel1 2635	. 2
3	1	a1i 11	. 2
4		riota2f.2	. . 3
5	4	a1i 11	. 2
6		id 22	. 2
7		riota2f.3	. . 3
8	7	adantl 466	. 2
9	2, 3, 5, 6, 8	riota2df 6278	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  F/wnf 1616  e.wcel 1818  F/_wnfc 2605  E!wreu 2809  iota_crio 6256

This theorem is referenced by:  riota2  6280  riotaprop  6281  riotass2  6284  riotass  6285  riotaxfrd  6288  cdlemksv2  36573  cdlemkuv2  36593  cdlemk36  36639

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-reu 2814  df-v 3111  df-sbc 3328  df-un 3480  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556  df-riota 6257