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Theorem bnj1400 29144
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1400.1
Assertion
Ref Expression
bnj1400
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem bnj1400
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dmuni 5071 . 2
2 df-iun 4087 . . 3
3 df-iun 4087 . . . 4
4 bnj1400.1 . . . . . . 7
54nfcii 2562 . . . . . 6
6 nfcv 2571 . . . . . 6
7 nfv 1629 . . . . . 6
8 nfv 1629 . . . . . 6
9 dmeq 5062 . . . . . . 7
109eleq2d 2502 . . . . . 6
115, 6, 7, 8, 10cbvrexf 2919 . . . . 5
1211abbii 2547 . . . 4
133, 12eqtr4i 2458 . . 3
142, 13eqtr4i 2458 . 2
151, 14eqtr4i 2458 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549   wceq 1652   wcel 1725  cab 2421  wrex 2698  cuni 4007  ciun 4085   cdm 4870 This theorem is referenced by:  bnj1398  29340  bnj1450  29356  bnj1498  29367  bnj1501  29373 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-3an 938  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-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-dm 4880
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