Theorem nfmpt1 3931

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 3901	. 2 |- ( x e. A |-> B ) = { <. x , z >. | ( x e. A /\ z = B ) }
2		nfopab1 3907	. 2 |- F/_ x { <. x , z >. | ( x e. A /\ z = B ) }
3	1, 2	nfcxfr 2225	1 |- F/_ x ( x e. A |-> B )

Syntax hints:   /\ wa 102   = wceq 1289   e. wcel 1438   F/_wnfc 2215   {copab 3898   |-> cmpt 3899

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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-opab 3900  df-mpt 3901

This theorem is referenced by:  nffvmpt1  5316  fvmptss2  5379  fvmptssdm  5387  fvmptdf  5390  mpteqb  5393  fvmptf  5395  ralrnmpt  5441  rexrnmpt  5442  f1ompt  5450  f1mpt  5550  fliftfun  5575  dom2lem  6489  mapxpen  6564