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Theorem bnj1146 29675
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1146.1
Assertion
Ref Expression
bnj1146
Distinct variable groups:   ,   ,,
Allowed substitution hint:   ()

Proof of Theorem bnj1146
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1769 . . . . . 6
2 bnj1146.1 . . . . . . . 8
32nfi 1682 . . . . . . 7
4 nfv 1769 . . . . . . 7
53, 4nfan 2031 . . . . . 6
6 eleq1 2537 . . . . . . 7
76anbi1d 719 . . . . . 6
81, 5, 7cbvex 2128 . . . . 5
9 df-rex 2762 . . . . 5
10 df-rex 2762 . . . . 5
118, 9, 103bitr4i 285 . . . 4
1211abbii 2587 . . 3
13 df-iun 4271 . . 3
14 df-iun 4271 . . 3
1512, 13, 143eqtr4i 2503 . 2
16 bnj1143 29674 . 2
1715, 16eqsstri 3448 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 376  wal 1450  wex 1671   wcel 1904  cab 2457  wrex 2757   wss 3390  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-or 377  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-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-v 3033  df-dif 3393  df-in 3397  df-ss 3404  df-nul 3723  df-iun 4271 This theorem is referenced by:  bnj1145  29874
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