Theorem hbsn 2450

Description: Bound-variable hypothesis builder for singletons.

Hypothesis

Ref	Expression
hbsn.1	|- (y e. A -> A.x y e. A)

Assertion

Ref	Expression
hbsn	|- (y e. {A} -> A.x y e. {A})

Distinct variable groups:   y,A   x,y

Proof of Theorem hbsn

Step	Hyp	Ref	Expression
1		dfsn2 2432	. 2 |- {A} = {A, A}
2		hbsn.1	. . 3 |- (y e. A -> A.x y e. A)
3	2, 2	hbpr 2438	. 2 |- (y e. {A, A} -> A.x y e. {A, A})
4	1, 3	hbxfr 1570	1 |- (y e. {A} -> A.x y e. {A})

Syntax hints:   -> wi 3  A.wal 958   e. wcel 962  {csn 2421  {cpr 2422

This theorem is referenced by:  hbop 2510  hbfv 3745

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 966  ax-gen 967  ax-8 968  ax-10 970  ax-12 972  ax-17 975  ax-4 977  ax-5o 979  ax-6o 982  ax-9o 1127  ax-10o 1144  ax-16 1214  ax-11o 1222  ax-ext 1464

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 985  df-sb 1176  df-clab 1470  df-cleq 1475  df-clel 1478  df-v 1819  df-un 2061  df-sn 2424  df-pr 2425

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