Theorem 19.37v 1910

Description: Version of 19.37 2100 with a dv condition, requiring fewer axioms. (Contributed by NM, 21-Jun-1993.)

Assertion

Ref	Expression
19.37v	|- ( E. x ( ph -> ps ) <-> ( ph -> E. x ps ) )

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem 19.37v

Step	Hyp	Ref	Expression
1		19.35 1805	. 2 |- ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) )
2		19.3v 1897	. . 3 |- ( A. x ph <-> ph )
3	2	imbi1i 339	. 2 |- ( ( A. x ph -> E. x ps ) <-> ( ph -> E. x ps ) )
4	1, 3	bitri 264	1 |- ( E. x ( ph -> ps ) <-> ( ph -> E. 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

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

This theorem is referenced by:  19.37iv  1911  eqvincg  3329  axrep5  4776  fvn0ssdmfun  6350  kmlem14  8985  kmlem15  8986  bnj132  30792  bnj1098  30854  bnj150  30946  bnj865  30993  bnj996  31025  bnj1021  31034  bnj1090  31047  bnj1176  31073  bj-axrep5  32792  cnvssco  37912  refimssco  37913  19.37vv  38584  pm11.61  38593  relopabVD  39137  rmoanim  41179