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Theorem opabbid 4262
 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 685 . . . . 5
52, 4exbid 1789 . . . 4
61, 5exbid 1789 . . 3
76abbidv 2549 . 2
8 df-opab 4259 . 2
9 df-opab 4259 . 2
107, 8, 93eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550  wnf 1553   wceq 1652  cab 2421  cop 3809  copab 4257 This theorem is referenced by:  opabbidv  4263  mpteq12f  4277  fnoprabg  6163  feqmptdf  24067  mpteq12d  25388 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-opab 4259
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