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Theorem opabbid 3822
 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 1507 . . . 4
61, 5exbid 1507 . . 3
76abbidv 2155 . 2
8 df-opab 3819 . 2
9 df-opab 3819 . 2
107, 8, 93eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243  wnf 1349  wex 1381  cab 2026  cop 3378  copab 3817 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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-opab 3819 This theorem is referenced by:  opabbidv  3823  mpteq12f  3837  fnoprabg  5602
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