Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj91 Structured version   Unicode version

Theorem bnj91 29159
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj91.1
bnj91.2
Assertion
Ref Expression
bnj91
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,)   (,)   (,)   (,,)

Proof of Theorem bnj91
StepHypRef Expression
1 bnj91.1 . . 3
21sbcbii 3208 . 2
3 bnj91.2 . . 3
43bnj525 29033 . 2
52, 4bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1652   wcel 1725  cvv 2948  wsbc 3153  c0 3620  cfv 5446   c-bnj14 28979 This theorem is referenced by:  bnj118  29167  bnj125  29170 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-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sbc 3154
 Copyright terms: Public domain W3C validator