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Theorem iota4an 5564
 Description: Theorem *14.23 in [WhiteheadRussell] p. 191. (Contributed by Andrew Salmon, 12-Jul-2011.)
Assertion
Ref Expression
iota4an

Proof of Theorem iota4an
StepHypRef Expression
1 iota4 5563 . 2
2 iotaex 5562 . . . 4
3 simpl 459 . . . . 5
43sbcth 3281 . . . 4
52, 4ax-mp 5 . . 3
6 sbcimg 3308 . . . 4
72, 6ax-mp 5 . . 3
85, 7mpbi 212 . 2
91, 8syl 17 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371   wcel 1886  weu 2298  cvv 3044  wsbc 3266  cio 5543 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430  ax-nul 4533 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-eu 2302  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ne 2623  df-ral 2741  df-rex 2742  df-v 3046  df-sbc 3267  df-dif 3406  df-un 3408  df-in 3410  df-ss 3417  df-nul 3731  df-sn 3968  df-pr 3970  df-uni 4198  df-iota 5545 This theorem is referenced by: (None)
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