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Theorem uniabio 5431
 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 188 . . . 4
3 df-sn 3822 . . . 4
42, 3syl6eqr 2488 . . 3
54unieqd 4028 . 2
6 vex 2961 . . 3
76unisn 4033 . 2
85, 7syl6eq 2486 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550   wceq 1653  cab 2424  csn 3816  cuni 4017 This theorem is referenced by:  iotaval  5432  iotauni  5433 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-v 2960  df-un 3327  df-sn 3822  df-pr 3823  df-uni 4018
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