Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj118 Structured version   Unicode version

Theorem bnj118 34028
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj118.1
bnj118.2
Assertion
Ref Expression
bnj118
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,)   (,)   (,)   (,,)

Proof of Theorem bnj118
StepHypRef Expression
1 bnj118.2 . 2
2 bnj118.1 . . 3
3 bnj105 33878 . . 3
42, 3bnj91 34020 . 2
51, 4bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wceq 1395  wsbc 3327  c0 3793  cfv 5594  c1o 7141   c-bnj14 33841 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pow 4634 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-sbc 3328  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-pw 4017  df-sn 4033  df-suc 4893  df-1o 7148 This theorem is referenced by:  bnj151  34036  bnj153  34039
 Copyright terms: Public domain W3C validator