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Theorem csbfv12g 5152
Description: Move class substitution in and out of a function value. (Contributed by NM, 11-Nov-2005.)
Assertion
Ref Expression
csbfv12g  C  [_  ]_ F `
 [_  ]_ F `  [_  ]_

Proof of Theorem csbfv12g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbiotag 4838 . . 3  C  [_  ]_ iota F  iota [.  ]. F
2 sbcbrg 3804 . . . . 5  C  [.  ]. F  [_  ]_ [_  ]_ F [_  ]_
3 csbconstg 2858 . . . . . 6  C  [_  ]_
43breq2d 3767 . . . . 5  C  [_  ]_ [_  ]_ F [_  ]_  [_  ]_ [_  ]_ F
52, 4bitrd 177 . . . 4  C  [.  ]. F  [_  ]_ [_  ]_ F
65iotabidv 4831 . . 3  C  iota [.  ]. F  iota [_  ]_ [_  ]_ F
71, 6eqtrd 2069 . 2  C  [_  ]_ iota F  iota [_  ]_ [_  ]_ F
8 df-fv 4853 . . 3  F `
 iota F
98csbeq2i 2870 . 2  [_  ]_ F `

[_  ]_ iota F
10 df-fv 4853 . 2  [_  ]_ F `  [_  ]_ 
iota [_  ]_ [_  ]_ F
117, 9, 103eqtr4g 2094 1  C  [_  ]_ F `
 [_  ]_ F `  [_  ]_
Colors of variables: wff set class
Syntax hints:   wi 4   wceq 1242   wcel 1390   [.wsbc 2758   [_csb 2846   class class class wbr 3755   iotacio 4808   ` cfv 4845
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-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  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-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-sbc 2759  df-csb 2847  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853
This theorem is referenced by:  csbfv2g  5153
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