Theorem bj-hbaeb 32806

Description: Biconditional version of hbae 2315. (Contributed by BJ, 6-Oct-2018.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-hbaeb	|- ( A. x x = y <-> A. z A. x x = y )

Proof of Theorem bj-hbaeb

Step	Hyp	Ref	Expression
1		bj-hbaeb2 32805	. 2 |- ( A. x x = y <-> A. x A. z x = y )
2		alcom 2037	. 2 |- ( A. x A. z x = y <-> A. z A. x x = y )
3	1, 2	bitri 264	1 |- ( A. x x = y <-> A. z A. x x = y )

Syntax hints:   <-> wb 196   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)