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Theorem csbief 2868
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 2867 . 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 1228   wcel 1374  wnfc 2147  Vcvv 2535  csb 2829
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-3an 875  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-sbc 2742  df-csb 2830
This theorem is referenced by:  csbing  3121  csbopabg  3809  pofun  4023  csbima12g  4613  csbiotag  4822  csbriotag  5404  csbov123g  5466  eqerlem  6048
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