Theorem nfmpt1 3879

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 3849	. 2 |- ( x e. A |-> B ) = { <. x , z >. | ( x e. A /\ z = B ) }
2		nfopab1 3855	. 2 |- F/_ x { <. x , z >. | ( x e. A /\ z = B ) }
3	1, 2	nfcxfr 2217	1 |- F/_ x ( x e. A |-> B )

Syntax hints:   /\ wa 102   = wceq 1285   e. wcel 1434   F/_wnfc 2207   {copab 3846   |-> cmpt 3847

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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-opab 3848  df-mpt 3849

This theorem is referenced by:  nffvmpt1  5217  fvmptss2  5279  fvmptssdm  5287  fvmptdf  5290  mpteqb  5293  fvmptf  5295  ralrnmpt  5341  rexrnmpt  5342  f1ompt  5352  f1mpt  5442  fliftfun  5467  dom2lem  6319