Theorem nfmpt21 5674

Description: Bound-variable hypothesis builder for an operation in maps-to notation. (Contributed by NM, 27-Aug-2013.)

Assertion

Ref	Expression
nfmpt21	|- F/_x(x e. A, y e. B |-> C)

Proof of Theorem nfmpt21

Dummy variable z is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-mpt2 5655	. 2 |- (x e. A, y e. B |-> C) = {<.<.x, y>., z>. | ((x e. A /\ y e. B) /\ z = C)}
2		nfoprab1 5547	. 2 |- F/_x{<.<.x, y>., z>. | ((x e. A /\ y e. B) /\ z = C)}
3	1, 2	nfcxfr 2487	1 |- F/_x(x e. A, y e. B |-> C)

Syntax hints:   /\ wa 358   = wceq 1642   e. wcel 1710   F/_wnfc 2477  {coprab 5528   |-> cmpt2 5654

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-oprab 5529  df-mpt2 5655

This theorem is referenced by:  ov2gf  5712