Theorem 19.36iv 1905

Description: Inference associated with 19.36v 1904. Version of 19.36i 2099 with a dv condition. (Contributed by NM, 5-Aug-1993.) Reduce dependencies on axioms. (Revised by Wolf Lammen, 17-Jan-2020.)

Hypothesis

Ref	Expression
19.36iv.1	|- E. x ( ph -> ps )

Assertion

Ref	Expression
19.36iv	|- ( A. x ph -> ps )

Distinct variable group:   ps, x

Allowed substitution hint:   ph( x)

Proof of Theorem 19.36iv

Step	Hyp	Ref	Expression
1		19.36iv.1	. 2 |- E. x ( ph -> ps )
2		19.36v 1904	. 2 |- ( E. x ( ph -> ps ) <-> ( A. x ph -> ps ) )
3	1, 2	mpbi 220	1 |- ( A. x ph -> ps )

Syntax hints:   -> wi 4   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

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

This theorem is referenced by:  spimv  2257  vtocl  3259  vtocl2  3261  vtocl3  3262  zfcndext  9435  bj-spimvv  32721