Theorem csbconstg 3155

Description: Substitution doesn't affect a constant B (in which x is not free). csbconstgf 3154 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 2386	. 2 |- F/_ x B
2	1	csbconstgf 3154	1 |- ( A e. V -> [_ A / x ]_ B = B )

Syntax hints:   -> wi 4   = wceq 1398   e. wcel 2205   [_csb 3141

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 2216

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-v 2817  df-sbc 3046  df-csb 3142

This theorem is referenced by:  sbcel1g  3160  sbceq1g  3161  sbcel2g  3162  sbceq2g  3163  csbidmg  3198  sbcbr12g  4170  sbcbr1g  4171  sbcbr2g  4172  sbcrel  4841  csbcnvg  4944  csbresg  5046  sbcfung  5381  csbfv12g  5715  csbfv2g  5716  elfvmptrab  5778  csbov12g  6098  csbov1g  6099  csbov2g  6100  csbwrdg  11279