Theorem nfmpt1 3871

Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by FL, 17-Feb-2008.)

Assertion

Ref	Expression
nfmpt1	|- F/_ x ( x e. A |-> B )

Proof of Theorem nfmpt1

Dummy variable z is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-mpt 3841	. 2 |- ( x e. A |-> B ) = { <. x , z >. | ( x e. A /\ z = B ) }
2		nfopab1 3847	. 2 |- F/_ x { <. x , z >. | ( x e. A /\ z = B ) }
3	1, 2	nfcxfr 2216	1 |- F/_ x ( x e. A |-> B )

Syntax hints:   /\ wa 102   = wceq 1284   e. wcel 1433   F/_wnfc 2206   {copab 3838   |-> cmpt 3839

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-opab 3840  df-mpt 3841

This theorem is referenced by:  nffvmpt1  5206  fvmptss2  5268  fvmptssdm  5276  fvmptdf  5279  mpteqb  5282  fvmptf  5284  ralrnmpt  5330  rexrnmpt  5331  f1ompt  5341  f1mpt  5431  fliftfun  5456  dom2lem  6275