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Theorem iota4an 4829
Description: Theorem *14.23 in [WhiteheadRussell] p. 191. (Contributed by Andrew Salmon, 12-Jul-2011.)
Assertion
Ref Expression
iota4an  [. iota  ].

Proof of Theorem iota4an
StepHypRef Expression
1 iota4 4828 . 2  [. iota  ].
2 euiotaex 4826 . . . 4  iota  _V
3 simpl 102 . . . . 5
43sbcth 2771 . . . 4 
iota  _V  [. iota  ].
52, 4syl 14 . . 3  [. iota  ].
6 sbcimg 2798 . . . 4 
iota  _V  [. iota  ].  [. iota  ].  [. iota  ].
72, 6syl 14 . . 3  [. iota  ].  [. iota  ].  [. iota  ].
85, 7mpbid 135 . 2  [. iota  ].  [. iota  ].
91, 8mpd 13 1  [. iota  ].
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wcel 1390  weu 1897   _Vcvv 2551   [.wsbc 2758   iotacio 4808
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-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-v 2553  df-sbc 2759  df-un 2916  df-sn 3373  df-pr 3374  df-uni 3572  df-iota 4810
This theorem is referenced by: (None)
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