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Theorem uniabio 4349
 Description: Part of Theorem 8.17 in [Quine] p. 56. This theorem serves as a lemma for the fundamental property of iota. (Contributed by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
uniabio
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem uniabio
StepHypRef Expression
1 abbi 2463 . . . . 5
21biimpi 186 . . . 4
3 df-sn 3741 . . . 4
42, 3syl6eqr 2403 . . 3
54unieqd 3902 . 2
6 vex 2862 . . 3
76unisn 3907 . 2
85, 7syl6eq 2401 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wal 1540   wceq 1642  cab 2339  csn 3737  cuni 3891 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-nan 1288  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-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-sn 3741  df-pr 3742  df-uni 3892 This theorem is referenced by:  iotaval  4350  iotauni  4351
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