Theorem csbconstgf 3057

Description: Substitution doesn't affect a constant B (in which x is not free). (Contributed by NM, 10-Nov-2005.)

Hypothesis

Ref	Expression
csbconstgf.1	|- F/_ x B

Assertion

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

Proof of Theorem csbconstgf

Step	Hyp	Ref	Expression
1		csbconstgf.1	. 2 |- F/_ x B
2		csbtt 3056	. 2 |- ( ( A e. V /\ F/_ x B ) -> [_ A / x ]_ B = B )
3	1, 2	mpan2 422	1 |- ( A e. V -> [_ A / x ]_ B = B )

Syntax hints:   -> wi 4   = wceq 1343   e. wcel 2136   F/_wnfc 2294   [_csb 3044

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 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2296  df-v 2727  df-sbc 2951  df-csb 3045

This theorem is referenced by:  csbconstg  3058