Theorem 19.37v 1943

Description: Special case of Theorem 19.37 of [Margaris] p. 90. (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		nfv 1683	. 2 |- F/ x ph
2	1	19.37 1915	1 |- ( E. x ( ph -> ps ) <-> ( ph -> E. x ps ) )

Syntax hints:   -> wi 4   <-> wb 184   E.wex 1596

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-12 1803

This theorem depends on definitions:  df-bi 185  df-ex 1597  df-nf 1600

This theorem is referenced by:  19.37aiv  1944  moanimOLD  2355  axrep5  4563  kmlem14  8543  kmlem15  8544  eqvincg  27078  19.37vv  30896  pm11.61  30905  rmoanim  31679  relopabVD  32799  bnj132  32877  bnj1098  32939  bnj150  33031  bnj865  33078  bnj996  33110  bnj1021  33119  bnj1090  33132  bnj1176  33158  bj-axrep5  33477