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Theorem bnj1146 29089
 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 1629 . . . . . 6
2 bnj1146.1 . . . . . . . 8
32nfi 1560 . . . . . . 7
4 nfv 1629 . . . . . . 7
53, 4nfan 1846 . . . . . 6
6 eleq1 2495 . . . . . . 7
76anbi1d 686 . . . . . 6
81, 5, 7cbvex 1983 . . . . 5
9 df-rex 2703 . . . . 5
10 df-rex 2703 . . . . 5
118, 9, 103bitr4i 269 . . . 4
1211abbii 2547 . . 3
13 df-iun 4087 . . 3
14 df-iun 4087 . . 3
1512, 13, 143eqtr4i 2465 . 2
16 bnj1143 29088 . 2
1715, 16eqsstri 3370 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wal 1549  wex 1550   wcel 1725  cab 2421  wrex 2698   wss 3312  ciun 4085 This theorem is referenced by:  bnj1145  29289 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-in 3319  df-ss 3326  df-nul 3621  df-iun 4087
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