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Theorem iota4an 4358
 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 4357 . 2
2 iotaex 4356 . . . 4
3 simpl 443 . . . . 5
43sbcth 3060 . . . 4
52, 4ax-mp 5 . . 3
6 sbcimg 3087 . . . 4
72, 6ax-mp 5 . . 3
85, 7mpbi 199 . 2
91, 8syl 15 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   wcel 1710  weu 2204  cvv 2859  wsbc 3046  cio 4337 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-rex 2620  df-v 2861  df-sbc 3047  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-sn 3741  df-pr 3742  df-uni 3892  df-iota 4339 This theorem is referenced by: (None)
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