Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ceqsalt Unicode version

Theorem ceqsalt 2597
 Description: Closed theorem version of ceqsalg 2599. (Contributed by NM, 28-Feb-2013.) (Revised by Mario Carneiro, 10-Oct-2016.)
Assertion
Ref Expression
ceqsalt
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem ceqsalt
StepHypRef Expression
1 elisset 2585 . . . 4
213ad2ant3 938 . . 3
3 bi1 115 . . . . . . 7
43imim3i 59 . . . . . 6
54al2imi 1363 . . . . 5
653ad2ant2 937 . . . 4
7 19.23t 1583 . . . . 5
873ad2ant1 936 . . . 4
96, 8sylibd 142 . . 3
102, 9mpid 41 . 2
11 bi2 125 . . . . . . 7
1211imim2i 12 . . . . . 6
1312com23 76 . . . . 5
1413alimi 1360 . . . 4
15143ad2ant2 937 . . 3
16 19.21t 1490 . . . 4
17163ad2ant1 936 . . 3
1815, 17mpbid 139 . 2
1910, 18impbid 124 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 102   w3a 896  wal 1257   wceq 1259  wnf 1365  wex 1397   wcel 1409 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3an 898  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-v 2576 This theorem is referenced by:  ceqsralt  2598
 Copyright terms: Public domain W3C validator