Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj121 Structured version   Unicode version

Theorem bnj121 32882
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj121.1
bnj121.2
bnj121.3
bnj121.4
Assertion
Ref Expression
bnj121
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,,)   (,)   (,)   (,,)   (,,)   (,,)

Proof of Theorem bnj121
StepHypRef Expression
1 bnj121.1 . . 3
21sbcbii 3384 . 2
3 bnj121.2 . 2
4 bnj105 32732 . . . . . . . 8
54bnj90 32730 . . . . . . 7
65bicomi 202 . . . . . 6
7 bnj121.3 . . . . . 6
8 bnj121.4 . . . . . 6
96, 7, 83anbi123i 1180 . . . . 5
10 sbc3an 3387 . . . . 5
119, 10bitr4i 252 . . . 4
1211imbi2i 312 . . 3
13 nfv 1678 . . . . 5
1413sbc19.21g 3397 . . . 4
154, 14ax-mp 5 . . 3
1612, 15bitr4i 252 . 2
172, 3, 163bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 968   wcel 1762  cvv 3106  wsbc 3324   wfn 5574  c1o 7113   w-bnj15 32699 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-9 1766  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438  ax-sep 4561  ax-nul 4569  ax-pow 4618 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ne 2657  df-v 3108  df-sbc 3325  df-dif 3472  df-un 3474  df-in 3476  df-ss 3483  df-nul 3779  df-pw 4005  df-sn 4021  df-suc 4877  df-fn 5582  df-1o 7120 This theorem is referenced by:  bnj150  32888  bnj153  32892
 Copyright terms: Public domain W3C validator