Theorem csbconstg 3109

Description: Substitution doesn't affect a constant B (in which x is not free). csbconstgf 3108 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 2349	. 2 |- F/_ x B
2	1	csbconstgf 3108	1 |- ( A e. V -> [_ A / x ]_ B = B )

Syntax hints:   -> wi 4   = wceq 1373   e. wcel 2177   [_csb 3095

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-v 2775  df-sbc 3001  df-csb 3096

This theorem is referenced by:  sbcel1g  3114  sbceq1g  3115  sbcel2g  3116  sbceq2g  3117  csbidmg  3152  sbcbr12g  4104  sbcbr1g  4105  sbcbr2g  4106  sbcrel  4766  csbcnvg  4867  csbresg  4968  sbcfung  5301  csbfv12g  5624  csbfv2g  5625  elfvmptrab  5685  csbov12g  5994  csbov1g  5995  csbov2g  5996  csbwrdg  11036