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Theorem oprabbid 5558
 Description: Equivalent wff's yield equal operation class abstractions (deduction rule). (Contributed by NM, 21-Feb-2004.) (Revised by Mario Carneiro, 24-Jun-2014.)
Hypotheses
Ref Expression
oprabbid.1
oprabbid.2
oprabbid.3
oprabbid.4
Assertion
Ref Expression
oprabbid
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,,)

Proof of Theorem oprabbid
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 oprabbid.1 . . . 4
2 oprabbid.2 . . . . 5
3 oprabbid.3 . . . . . 6
4 oprabbid.4 . . . . . . 7
54anbi2d 437 . . . . . 6
63, 5exbid 1507 . . . . 5
72, 6exbid 1507 . . . 4
81, 7exbid 1507 . . 3
98abbidv 2155 . 2
10 df-oprab 5516 . 2
11 df-oprab 5516 . 2
129, 10, 113eqtr4g 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  coprab 5513 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-oprab 5516 This theorem is referenced by:  oprabbidv  5559  mpt2eq123  5564
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