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Theorem bnj956 29660
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj956.1
Assertion
Ref Expression
bnj956

Proof of Theorem bnj956
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj956.1 . . . 4
2 eleq2 2538 . . . . . . . 8
32anbi1d 719 . . . . . . 7
43alimi 1692 . . . . . 6
5 exbi 1724 . . . . . 6
64, 5syl 17 . . . . 5
7 df-rex 2762 . . . . 5
8 df-rex 2762 . . . . 5
96, 7, 83bitr4g 296 . . . 4
101, 9syl 17 . . 3
1110abbidv 2589 . 2
12 df-iun 4271 . 2
13 df-iun 4271 . 2
1411, 12, 133eqtr4g 2530 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450   wceq 1452  wex 1671   wcel 1904  cab 2457  wrex 2757  ciun 4269 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-rex 2762  df-iun 4271 This theorem is referenced by:  bnj1316  29704  bnj953  29822  bnj1000  29824  bnj966  29827
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