Theorem bnj63 12432

Description: First-order logic and set theory.

Assertion

Ref	Expression
bnj63	|- (x Fn A <-> x e. fns A)

Distinct variable group:   x,A

Proof of Theorem bnj63

Step	Hyp	Ref	Expression
1		df-bnj16 12022	. . 3 |- fns A = {x | x Fn A}
2	1	eleq2i 1961	. 2 |- (x e. fns A <-> x e. {x | x Fn A})
3		abid 1873	. 2 |- (x e. {x | x Fn A} <-> x Fn A)
4	2, 3	bitr2i 191	1 |- (x Fn A <-> x e. fns A)

Syntax hints:   <-> wb 163   e. wcel 1300  {cab 1871   Fn wfn 3993   fns syn-bnj16 12021

This theorem is referenced by:  bnj62OLD 12434

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-12 1310  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-ext 1865

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-bnj16 12022

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