Theorem csbconstgf 3137

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 3136	. 2 |- ( ( A e. V /\ F/_ x B ) -> [_ A / x ]_ B = B )
3	1, 2	mpan2 425	1 |- ( A e. V -> [_ A / x ]_ B = B )

Syntax hints:   -> wi 4   = wceq 1395   e. wcel 2200   F/_wnfc 2359   [_csb 3124

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-sbc 3029  df-csb 3125

This theorem is referenced by:  csbconstg  3138