Theorem bj-biexal1 32696

Description: A general FOL biconditional that generalizes 19.9ht 2143 among others. For this and the following theorems, see also 19.35 1805, 19.21 2075, 19.23 2080. (Contributed by BJ, 20-Oct-2019.)

Assertion

Ref	Expression
bj-biexal1	|- ( A. x ( ph -> A. x ps ) <-> ( E. x ph -> A. x ps ) )

Proof of Theorem bj-biexal1

Step	Hyp	Ref	Expression
1		nfa1 2028	. 2 |- F/ x A. x ps
2	1	19.23 2080	1 |- ( A. x ( ph -> A. x ps ) <-> ( E. x ph -> A. x ps ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   E.wex 1704

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-12 2047

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

This theorem is referenced by:  bj-biexal3  32698