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Theorem riota2f 5432
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  F/_
riota2f.2  F/
riota2f.3
Assertion
Ref Expression
riota2f  iota_
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem riota2f
StepHypRef Expression
1 riota2f.1 . . 3  F/_
21nfel1 2185 . 2  F/
31a1i 9 . 2  F/_
4 riota2f.2 . . 3  F/
54a1i 9 . 2  F/
6 id 19 . 2
7 riota2f.3 . . 3
87adantl 262 . 2
92, 3, 5, 6, 8riota2df 5431 1  iota_
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242   F/wnf 1346   wcel 1390   F/_wnfc 2162  wreu 2302   iota_crio 5410
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-reu 2307  df-v 2553  df-sbc 2759  df-un 2916  df-sn 3373  df-pr 3374  df-uni 3572  df-iota 4810  df-riota 5411
This theorem is referenced by:  riota2  5433  riotaprop  5434  riotass2  5437  riotass  5438
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