Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj23 Structured version   Visualization version   Unicode version

Theorem bnj23 29524
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Mario Carneiro, 22-Dec-2016.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj23.1
Assertion
Ref Expression
bnj23
Distinct variable groups:   ,   ,,   ,,,   ,,,
Allowed substitution hints:   (,,,)   ()   ()   ()

Proof of Theorem bnj23
StepHypRef Expression
1 vex 3048 . . . . 5
2 sbcng 3308 . . . . 5
31, 2ax-mp 5 . . . 4
4 bnj23.1 . . . . . . . 8
54eleq2i 2521 . . . . . . 7
6 nfcv 2592 . . . . . . . 8
76elrabsf 3306 . . . . . . 7
85, 7bitri 253 . . . . . 6
9 breq1 4405 . . . . . . . 8
109notbid 296 . . . . . . 7
1110rspccv 3147 . . . . . 6
128, 11syl5bir 222 . . . . 5
1312expdimp 439 . . . 4
143, 13syl5bir 222 . . 3
1514con4d 109 . 2
1615ralrimiva 2802 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wa 371   wceq 1444   wcel 1887  wral 2737  crab 2741  cvv 3045  wsbc 3267   class class class wbr 4402 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ral 2742  df-rab 2746  df-v 3047  df-sbc 3268  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-if 3882  df-sn 3969  df-pr 3971  df-op 3975  df-br 4403 This theorem is referenced by:  bnj110  29669
 Copyright terms: Public domain W3C validator