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Theorem csbeq2d 2868
Description: Formula-building deduction rule for class substitution. (Contributed by NM, 22-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)
Hypotheses
Ref Expression
csbeq2d.1  F/
csbeq2d.2  C
Assertion
Ref Expression
csbeq2d  [_  ]_  [_  ]_ C

Proof of Theorem csbeq2d
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq2d.1 . . . 4  F/
2 csbeq2d.2 . . . . 5  C
32eleq2d 2104 . . . 4  C
41, 3sbcbid 2810 . . 3  [.  ].  [.  ].  C
54abbidv 2152 . 2  {  |  [.  ].  }  {  |  [.  ].  C }
6 df-csb 2847 . 2  [_  ]_  {  |  [.  ].  }
7 df-csb 2847 . 2  [_  ]_ C  {  |  [.  ].  C }
85, 6, 73eqtr4g 2094 1  [_  ]_  [_  ]_ C
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   F/wnf 1346   wcel 1390   {cab 2023   [.wsbc 2758   [_csb 2846
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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-sbc 2759  df-csb 2847
This theorem is referenced by:  csbeq2dv  2869
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