Theorem csbconstg 3045

Description: Substitution doesn't affect a constant B (in which x is not free). csbconstgf 3044 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 2299	. 2 |- F/_ x B
2	1	csbconstgf 3044	1 |- ( A e. V -> [_ A / x ]_ B = B )

Syntax hints:   -> wi 4   = wceq 1335   e. wcel 2128   [_csb 3031

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-sbc 2938  df-csb 3032

This theorem is referenced by:  sbcel1g  3050  sbceq1g  3051  sbcel2g  3052  sbceq2g  3053  csbidmg  3087  sbcbr12g  4020  sbcbr1g  4021  sbcbr2g  4022  sbcrel  4673  csbcnvg  4771  csbresg  4870  sbcfung  5195  csbfv12g  5505  csbfv2g  5506  elfvmptrab  5564  csbov12g  5861  csbov1g  5862  csbov2g  5863