Theorem hbra1 2663

Description: x is not free in A.x e. Aph. (Contributed by NM, 18-Oct-1996.)

Assertion

Ref	Expression
hbra1	|- (A.x e. A ph -> A.xA.x e. A ph)

Proof of Theorem hbra1

Step	Hyp	Ref	Expression
1		df-ral 2619	. 2 |- (A.x e. A ph <-> A.x(x e. A -> ph))
2		hba1 1786	. 2 |- (A.x(x e. A -> ph) -> A.xA.x(x e. A -> ph))
3	1, 2	hbxfrbi 1568	1 |- (A.x e. A ph -> A.xA.x e. A ph)

Syntax hints:   -> wi 4  A.wal 1540   e. wcel 1710  A.wral 2614

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-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-ral 2619

This theorem is referenced by: (None)