Theorem nfmpt1 4098

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 4068	. 2 |- ( x e. A |-> B ) = { <. x , z >. | ( x e. A /\ z = B ) }
2		nfopab1 4074	. 2 |- F/_ x { <. x , z >. | ( x e. A /\ z = B ) }
3	1, 2	nfcxfr 2316	1 |- F/_ x ( x e. A |-> B )

Syntax hints:   /\ wa 104   = wceq 1353   e. wcel 2148   F/_wnfc 2306   {copab 4065   |-> cmpt 4066

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-opab 4067  df-mpt 4068

This theorem is referenced by:  nffvmpt1  5528  fvmptss2  5594  fvmptssdm  5603  fvmptdf  5606  mpteqb  5609  fvmptf  5611  ralrnmpt  5661  rexrnmpt  5662  f1ompt  5670  f1mpt  5775  fliftfun  5800  dom2lem  6775  mapxpen  6851  mkvprop  7159  cc3  7270  nfcprod1  11565  cnmpt11  13971  lgseisenlem2  14639