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Theorem sbcopg 25131
 Description: Distribution of class substitution over ordered pairs. (Contributed by Drahflow, 25-Sep-2015.) (Revised by Mario Carneiro, 29-Oct-2015.)
Assertion
Ref Expression
sbcopg
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem sbcopg
StepHypRef Expression
1 nfcsb1v 3285 . . . 4
2 nfcsb1v 3285 . . . 4
31, 2nfop 4002 . . 3
43a1i 11 . 2
5 csbeq1a 3261 . . 3
6 csbeq1a 3261 . . 3
75, 6opeq12d 3994 . 2
84, 7csbiegf 3293 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1726  wnfc 2561  cvv 2958  csb 3253  cop 3819 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825
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