Theorem csbconstg 3142

Description: Substitution doesn't affect a constant B (in which x is not free). csbconstgf 3141 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 2375	. 2 |- F/_ x B
2	1	csbconstgf 3141	1 |- ( A e. V -> [_ A / x ]_ B = B )

Syntax hints:   -> wi 4   = wceq 1398   e. wcel 2202   [_csb 3128

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-v 2805  df-sbc 3033  df-csb 3129

This theorem is referenced by:  sbcel1g  3147  sbceq1g  3148  sbcel2g  3149  sbceq2g  3150  csbidmg  3185  sbcbr12g  4149  sbcbr1g  4150  sbcbr2g  4151  sbcrel  4818  csbcnvg  4920  csbresg  5022  sbcfung  5357  csbfv12g  5688  csbfv2g  5689  elfvmptrab  5751  csbov12g  6068  csbov1g  6069  csbov2g  6070  csbwrdg  11190