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Theorem csbconstg 2921
Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 2920 with distinct variable requirement. (Contributed by Alan Sare, 22-Jul-2012.)
Assertion
Ref Expression
csbconstg (𝐴𝑉𝐴 / 𝑥𝐵 = 𝐵)
Distinct variable group:   𝑥,𝐵
Allowed substitution hints:   𝐴(𝑥)   𝑉(𝑥)

Proof of Theorem csbconstg
StepHypRef Expression
1 nfcv 2220 . 2 𝑥𝐵
21csbconstgf 2920 1 (𝐴𝑉𝐴 / 𝑥𝐵 = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1285  wcel 1434  csb 2909
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-sbc 2817  df-csb 2910
This theorem is referenced by:  sbcel1g  2926  sbceq1g  2927  sbcel2g  2928  sbceq2g  2929  csbidmg  2959  sbcbr12g  3843  sbcbr1g  3844  sbcbr2g  3845  sbcrel  4452  csbcnvg  4547  csbresg  4643  sbcfung  4955  csbfv12g  5241  csbfv2g  5242  csbov12g  5575  csbov1g  5576  csbov2g  5577
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