Theorem nfmpt1 4097

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 4067	. 2 |- ( x e. A |-> B ) = { <. x , z >. | ( x e. A /\ z = B ) }
2		nfopab1 4073	. 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 4064   |-> cmpt 4065

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 4066  df-mpt 4067

This theorem is referenced by:  nffvmpt1  5527  fvmptss2  5592  fvmptssdm  5601  fvmptdf  5604  mpteqb  5607  fvmptf  5609  ralrnmpt  5659  rexrnmpt  5660  f1ompt  5668  f1mpt  5772  fliftfun  5797  dom2lem  6772  mapxpen  6848  mkvprop  7156  cc3  7267  nfcprod1  11562  cnmpt11  13786  lgseisenlem2  14454