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Theorem uniabio 5575
 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 2548 . . . . 5
21biimpi 197 . . . 4
3 df-sn 3999 . . . 4
42, 3syl6eqr 2481 . . 3
54unieqd 4229 . 2
6 vex 3083 . . 3
76unisn 4234 . 2
85, 7syl6eq 2479 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187  wal 1435   wceq 1437  cab 2407  csn 3998  cuni 4219 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-rex 2777  df-v 3082  df-un 3441  df-sn 3999  df-pr 4001  df-uni 4220 This theorem is referenced by:  iotaval  5576  iotauni  5577
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