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Theorem dfiota2 4340
 Description: Alternate definition for descriptions. Definition 8.18 in [Quine] p. 56. (Contributed by Andrew Salmon, 30-Jun-2011.)
Assertion
Ref Expression
dfiota2
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem dfiota2
StepHypRef Expression
1 df-iota 4339 . 2
2 df-sn 3741 . . . . . 6
32eqeq2i 2363 . . . . 5
4 abbi 2463 . . . . 5
53, 4bitr4i 243 . . . 4
65abbii 2465 . . 3
76unieqi 3901 . 2
81, 7eqtri 2373 1
 Colors of variables: wff setvar class Syntax hints:   wb 176  wal 1540   wceq 1642  cab 2339  csn 3737  cuni 3891  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 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-sn 3741  df-uni 3892  df-iota 4339 This theorem is referenced by:  nfiota1  4341  nfiotad  4342  cbviota  4344  sb8iota  4346  iotaval  4350  iotanul  4354  eqtfinrelk  4486  fv2  5324  tcfnex  6244
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