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Theorem csbief 2885
Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by NM, 26-Nov-2005.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypotheses
Ref Expression
csbief.1 A V
csbief.2 x𝐶
csbief.3 (x = AB = 𝐶)
Assertion
Ref Expression
csbief A / xB = 𝐶
Distinct variable group:   x,A
Allowed substitution hints:   B(x)   𝐶(x)

Proof of Theorem csbief
StepHypRef Expression
1 csbief.1 . 2 A V
2 csbief.2 . . . 4 x𝐶
32a1i 9 . . 3 (A V → x𝐶)
4 csbief.3 . . 3 (x = AB = 𝐶)
53, 4csbiegf 2884 . 2 (A V → A / xB = 𝐶)
61, 5ax-mp 7 1 A / xB = 𝐶
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242   wcel 1390  wnfc 2162  Vcvv 2551  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-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-bnd 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-v 2553  df-sbc 2759  df-csb 2847
This theorem is referenced by:  csbing  3138  csbopabg  3826  pofun  4040  csbima12g  4629  csbiotag  4838  csbriotag  5423  csbov123g  5485  eqerlem  6073
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