Theorem bj-19.21t 32817

Description: Proof of 19.21t 2073 from stdpc5t 32814. (Contributed by BJ, 15-Sep-2018.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-19.21t	|- ( F/ x ph -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )

Proof of Theorem bj-19.21t

Step	Hyp	Ref	Expression
1		stdpc5t 32814	. 2 |- ( F/ x ph -> ( A. x ( ph -> ps ) -> ( ph -> A. x ps ) ) )
2		19.9t 2071	. . . 4 |- ( F/ x ph -> ( E. x ph <-> ph ) )
3	2	imbi1d 331	. . 3 |- ( F/ x ph -> ( ( E. x ph -> A. x ps ) <-> ( ph -> A. x ps ) ) )
4		19.38 1766	. . 3 |- ( ( E. x ph -> A. x ps ) -> A. x ( ph -> ps ) )
5	3, 4	syl6bir 244	. 2 |- ( F/ x ph -> ( ( ph -> A. x ps ) -> A. x ( ph -> ps ) ) )
6	1, 5	impbid 202	1 |- ( F/ x ph -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481   E.wex 1704   F/wnf 1708

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-12 2047

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

This theorem is referenced by: (None)