Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj538 Structured version   Unicode version

Theorem bnj538 29108
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj538.1
Assertion
Ref Expression
bnj538
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem bnj538
StepHypRef Expression
1 df-ral 2710 . . 3
21sbcbii 3216 . 2
3 bnj538.1 . . . . . 6
4 sbcimg 3202 . . . . . 6
53, 4ax-mp 8 . . . . 5
63bnj525 29106 . . . . . 6
76imbi1i 316 . . . . 5
85, 7bitri 241 . . . 4
98albii 1575 . . 3
10 sbcal 3208 . . 3
11 df-ral 2710 . . 3
129, 10, 113bitr4i 269 . 2
132, 12bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549   wcel 1725  wral 2705  cvv 2956  wsbc 3161 This theorem is referenced by:  bnj92  29233  bnj539  29262  bnj540  29263 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-v 2958  df-sbc 3162
 Copyright terms: Public domain W3C validator