Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  csbfv2g Structured version   Unicode version

Theorem csbfv2g 5743
 Description: Move class substitution in and out of a function value. (Contributed by NM, 10-Nov-2005.)
Assertion
Ref Expression
csbfv2g
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem csbfv2g
StepHypRef Expression
1 csbfv12g 5741 . 2
2 csbconstg 3267 . . 3
32fveq1d 5733 . 2
41, 3eqtrd 2470 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1726  csb 3253  cfv 5457 This theorem is referenced by:  csbfvg  5744  sumeq2ii  12492  fsumabs  12585  iuninc  24016  prodeq2ii  25244  fprodabs  25302  cdlemk39s  31810 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-ral 2712  df-rex 2713  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  df-uni 4018  df-br 4216  df-iota 5421  df-fv 5465
 Copyright terms: Public domain W3C validator