Theorem nfmpt1 4224

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 4194	. 2 |- ( x e. A |-> B ) = { <. x , z >. | ( x e. A /\ z = B ) }
2		nfopab1 4200	. 2 |- F/_ x { <. x , z >. | ( x e. A /\ z = B ) }
3	1, 2	nfcxfr 2389	1 |- F/_ x ( x e. A |-> B )

This proof depends on syntax axioms:   /\ wa 104   = wceq 1402   e. wcel 2209   F/_wnfc 2379   {copab 4191   |-> cmpt 4192

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-opab 4193  df-mpt 4194

This theorem is used by:  nffvmpt1  5706  fvmptss2  5780  fvmptssdm  5790  fvmptdf  5793  mpteqb  5796  fvmptf  5798  ralrnmpt  5850  rexrnmpt  5851  f1ompt  5859  f1mpt  5977  fliftfun  6002  dom2lem  7058  mapxpen  7148  mkvprop  7498  cc3  7634  nfcprod1  12321  ballotfilem7  13279  cnmpt11  15384  lgseisenlem2  16190