Mathbox for Thierry Arnoux < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  spc2d Structured version   Unicode version

Theorem spc2d 28105
 Description: Specialization with 2 quantifiers, using implicit substitution. (Contributed by Thierry Arnoux, 23-Aug-2017.)
Hypotheses
Ref Expression
spc2ed.x
spc2ed.y
spc2ed.1
Assertion
Ref Expression
spc2d
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)   (,)

Proof of Theorem spc2d
StepHypRef Expression
1 2nalexn 1694 . . 3
21con1bii 332 . 2
3 spc2ed.x . . . . 5
43nfn 1960 . . . 4
5 spc2ed.y . . . . 5
65nfn 1960 . . . 4
7 spc2ed.1 . . . . 5
87notbid 295 . . . 4
94, 6, 8spc2ed 28104 . . 3
109con1d 127 . 2
112, 10syl5bir 221 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187   wa 370  wal 1435   wceq 1437  wex 1657  wnf 1661   wcel 1872 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-v 3082 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator