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Theorem iota1 5567
 Description: Property of iota. (Contributed by NM, 23-Aug-2011.) (Revised by Mario Carneiro, 23-Dec-2016.)
Assertion
Ref Expression
iota1

Proof of Theorem iota1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-eu 2323 . 2
2 sp 1957 . . . . 5
3 iotaval 5564 . . . . . 6
43eqeq2d 2481 . . . . 5
52, 4bitr4d 264 . . . 4
6 eqcom 2478 . . . 4
75, 6syl6bb 269 . . 3
87exlimiv 1784 . 2
91, 8sylbi 200 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189  wal 1450   wceq 1452  wex 1671  weu 2319  cio 5551 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-rex 2762  df-v 3033  df-sbc 3256  df-un 3395  df-sn 3960  df-pr 3962  df-uni 4191  df-iota 5553 This theorem is referenced by:  iota2df  5577  sniota  5580  tz6.12-1  5895  opabiota  5943  riota1  6288  riota1a  6289  erovlem  7477  gsumval3lem2  17618  bnj1366  29713
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