Theorem hbre1 1239

Description: x is not free in E.x e. Aph.

Assertion

Ref	Expression
hbre1	|- (E.x e. A ph -> A.xE.x e. A ph)

Proof of Theorem hbre1

Step	Hyp	Ref	Expression
1		hbe1 709	. 2 |- (E.x(x e. A /\ ph) -> A.xE.x(x e. A /\ ph))
2		df-rex 1206	. 2 |- (E.x e. A ph <-> E.x(x e. A /\ ph))
3	2	bial 695	. 2 |- (A.xE.x e. A ph <-> A.xE.x(x e. A /\ ph))
4	1, 2, 3	3imtr4 192	1 |- (E.x e. A ph -> A.xE.x e. A ph)

Syntax hints:   -> wi 2   /\ wa 196  A.wal 672  E.wex 678   e. wcel 1092  E.wrex 1202

This theorem is referenced by:  hbiu1 2012  onfr 2237  zfregcl 3446  scott0 3542  chcmh 5148  atom1d 5750

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-rex 1206

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