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Theorem bnj956 29221
 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 2499 . . . . . . . 8
32anbi1d 687 . . . . . . 7
43alimi 1569 . . . . . 6
5 exbi 1592 . . . . . 6
64, 5syl 16 . . . . 5
7 df-rex 2713 . . . . 5
8 df-rex 2713 . . . . 5
96, 7, 83bitr4g 281 . . . 4
101, 9syl 16 . . 3
1110abbidv 2552 . 2
12 df-iun 4097 . 2
13 df-iun 4097 . 2
1411, 12, 133eqtr4g 2495 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551   wceq 1653   wcel 1726  cab 2424  wrex 2708  ciun 4095 This theorem is referenced by:  bnj1316  29266  bnj953  29384  bnj1000  29386  bnj966  29389 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-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-rex 2713  df-iun 4097
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