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Theorem bnj919 29650
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj919.1
bnj919.2
bnj919.3
bnj919.4
bnj919.5
Assertion
Ref Expression
bnj919
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   ()   ()

Proof of Theorem bnj919
StepHypRef Expression
1 bnj919.4 . 2
2 bnj919.1 . . 3
32sbcbii 3311 . 2
4 bnj919.5 . . 3
5 df-bnj17 29564 . . . . 5
6 nfv 1769 . . . . . . 7
7 nfv 1769 . . . . . . 7
8 bnj919.2 . . . . . . . 8
9 nfsbc1v 3275 . . . . . . . 8
108, 9nfxfr 1704 . . . . . . 7
116, 7, 10nf3an 2033 . . . . . 6
12 bnj919.3 . . . . . . 7
13 nfsbc1v 3275 . . . . . . 7
1412, 13nfxfr 1704 . . . . . 6
1511, 14nfan 2031 . . . . 5
165, 15nfxfr 1704 . . . 4
17 eleq1 2537 . . . . . 6
18 fneq2 5675 . . . . . . 7
19 sbceq1a 3266 . . . . . . . 8
2019, 8syl6bbr 271 . . . . . . 7
21 sbceq1a 3266 . . . . . . . 8
2221, 12syl6bbr 271 . . . . . . 7
2318, 20, 223anbi123d 1365 . . . . . 6
2417, 23anbi12d 725 . . . . 5
25 bnj252 29580 . . . . 5
26 bnj252 29580 . . . . 5
2724, 25, 263bitr4g 296 . . . 4
2816, 27sbciegf 3287 . . 3
294, 28ax-mp 5 . 2
301, 3, 293bitri 279 1
 Colors of variables: wff setvar class Syntax hints:   wb 189   wa 376   w3a 1007   wceq 1452   wcel 1904  cvv 3031  wsbc 3255   wfn 5584   w-bnj17 29563 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-3an 1009  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-v 3033  df-sbc 3256  df-fn 5592  df-bnj17 29564 This theorem is referenced by:  bnj910  29831  bnj999  29840  bnj907  29848
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