Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj90 Structured version   Unicode version

Theorem bnj90 33483
 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
bnj90.1
Assertion
Ref Expression
bnj90
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem bnj90
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj90.1 . 2
2 fneq2 5656 . . 3
3 fneq2 5656 . . 3
42, 3sbcie2g 3345 . 2
51, 4ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wcel 1802  cvv 3093  wsbc 3311   wfn 5569 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-12 1838  ax-13 1983  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-v 3095  df-sbc 3312  df-fn 5577 This theorem is referenced by:  bnj121  33635  bnj130  33639  bnj207  33646
 Copyright terms: Public domain W3C validator