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Theorem csbconstg 2943
Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). csbconstgf 2942 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 2228 . 2 𝑥𝐵
21csbconstgf 2942 1 (𝐴𝑉𝐴 / 𝑥𝐵 = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1289  wcel 1438  csb 2931
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-sbc 2839  df-csb 2932
This theorem is referenced by:  sbcel1g  2948  sbceq1g  2949  sbcel2g  2950  sbceq2g  2951  csbidmg  2982  sbcbr12g  3887  sbcbr1g  3888  sbcbr2g  3889  sbcrel  4512  csbcnvg  4608  csbresg  4704  sbcfung  5025  csbfv12g  5324  csbfv2g  5325  csbov12g  5670  csbov1g  5671  csbov2g  5672
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