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Theorem bnj106 29176
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj106.1
bnj106.2
Assertion
Ref Expression
bnj106
Distinct variable groups:   ,,   ,,,   ,,   ,,
Allowed substitution hints:   (,,,)   (,)   (,)   ()

Proof of Theorem bnj106
StepHypRef Expression
1 bnj106.1 . . . 4
2 bnj105 29026 . . . 4
31, 2bnj92 29170 . . 3
43sbcbii 3208 . 2
5 bnj106.2 . . 3
6 fveq1 5719 . . . . . 6
7 fveq1 5719 . . . . . . 7
87bnj1113 29093 . . . . . 6
96, 8eqeq12d 2449 . . . . 5
109imbi2d 308 . . . 4
1110ralbidv 2717 . . 3
125, 11sbcie 3187 . 2
134, 12bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  wral 2697  cvv 2948  wsbc 3153  ciun 4085   csuc 4575  com 4837  cfv 5446  c1o 6709   c-bnj14 28989 This theorem is referenced by:  bnj126  29181 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pow 4369 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-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-pw 3793  df-sn 3812  df-uni 4008  df-iun 4087  df-br 4205  df-suc 4579  df-iota 5410  df-fv 5454  df-1o 6716
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