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Theorem uniabio 6235
 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 2368 . . . . 5
21biimpi 188 . . . 4
3 df-sn 3620 . . . 4
42, 3syl6eqr 2308 . . 3
54unieqd 3812 . 2
6 vex 2766 . . 3
76unisn 3817 . 2
85, 7syl6eq 2306 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178  wal 1532   wceq 1619  cab 2244  csn 3614  cuni 3801 This theorem is referenced by:  iotaval  6236  iotauni  6237 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2239 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-rex 2524  df-v 2765  df-un 3132  df-sn 3620  df-pr 3621  df-uni 3802
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