Theorem hbcmpt 10452

Description: Bound-variable hypothesis builder for the "maps to" notation.

Assertion

Ref	Expression
hbcmpt	|- (y e. (x e. A |-> B) -> A.x y e. (x e. A |-> B))

Distinct variable group:   x,y

Proof of Theorem hbcmpt

Step	Hyp	Ref	Expression
1		df-mpt 4079	. 2 |- (x e. A |-> B) = {<.x, z>. | (x e. A /\ z = B)}
2		hbopab1 2819	. 2 |- (y e. {<.x, z>. | (x e. A /\ z = B)} -> A.x y e. {<.x, z>. | (x e. A /\ z = B)})
3	1, 2	hbxfr 1566	1 |- (y e. (x e. A |-> B) -> A.x y e. (x e. A |-> B))

Syntax hints:   -> wi 3   /\ wa 223  A.wal 956   = wceq 958   e. wcel 960  {copab 2671   e. cmpt 4077

This theorem is referenced by:  cnvtr 10609

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 983  df-sb 1174  df-clab 1467  df-cleq 1472  df-clel 1475  df-opab 2672  df-mpt 4079

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