Theorem csbconstgf 3160

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 3159	. 2 |- ( ( A e. V /\ F/_ x B ) -> [_ A / x ]_ B = B )
3	1, 2	mpan2 429	1 |- ( A e. V -> [_ A / x ]_ B = B )

Syntax hints:   -> wi 4   = wceq 1402   e. wcel 2209   F/_wnfc 2379   [_csb 3147

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-sbc 3052  df-csb 3148

This theorem is referenced by:  csbconstg  3161