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Theorem opabbid 4514
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 703 . . . . 5
52, 4exbid 1886 . . . 4
61, 5exbid 1886 . . 3
76abbidv 2593 . 2
8 df-opab 4511 . 2
9 df-opab 4511 . 2
107, 8, 93eqtr4g 2523 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  F/wnf 1616  {cab 2442  <.cop 4035  {copab 4509
This theorem is referenced by:  opabbidv  4515  mpteq12f  4528  fnoprabg  6403  feqmptdf  27501  mpteq12d  29202
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-opab 4511
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