Theorem csbconstg 2920

Description: Substitution doesn't affect a constant B (in which x is not free). csbconstgf 2919 with distinct variable requirement. (Contributed by Alan Sare, 22-Jul-2012.)

Assertion

Ref	Expression
csbconstg	|- ( A e. V -> [_ A / x ]_ B = B )

Distinct variable group:   x, B

Allowed substitution hints:   A( x)   V( x)

Proof of Theorem csbconstg

Step	Hyp	Ref	Expression
1		nfcv 2219	. 2 |- F/_ x B
2	1	csbconstgf 2919	1 |- ( A e. V -> [_ A / x ]_ B = B )

Syntax hints:   -> wi 4   = wceq 1284   e. wcel 1433   [_csb 2908

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 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-sbc 2816  df-csb 2909

This theorem is referenced by:  sbcel1g  2925  sbceq1g  2926  sbcel2g  2927  sbceq2g  2928  csbidmg  2958  sbcbr12g  3835  sbcbr1g  3836  sbcbr2g  3837  sbcrel  4444  csbcnvg  4537  csbresg  4633  sbcfung  4945  csbfv12g  5230  csbfv2g  5231  csbov12g  5564  csbov1g  5565  csbov2g  5566