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

Theorem opabbid 3813
 Description: Equivalent wff's yield equal ordered-pair class abstractions (deduction rule). (Contributed by NM, 21-Feb-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Hypotheses
Ref Expression
opabbid.1
opabbid.2
opabbid.3
Assertion
Ref Expression
opabbid

Proof of Theorem opabbid
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 opabbid.1 . . . 4
2 opabbid.2 . . . . 5
3 opabbid.3 . . . . . 6
43anbi2d 437 . . . . 5
52, 4exbid 1504 . . . 4
61, 5exbid 1504 . . 3
76abbidv 2152 . 2
8 df-opab 3810 . 2
9 df-opab 3810 . 2
107, 8, 93eqtr4g 2094 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1242  wnf 1346  wex 1378  cab 2023  cop 3370  copab 3808 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-opab 3810 This theorem is referenced by:  opabbidv  3814  mpteq12f  3828  fnoprabg  5544
 Copyright terms: Public domain W3C validator