Theorem 19.23v 1863

Description: Special case of Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 28-Jun-1998.)

Assertion

Ref	Expression
19.23v	|- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Distinct variable group:   ps, x

Allowed substitution hint:   ph( x)

Proof of Theorem 19.23v

Step	Hyp	Ref	Expression
1		ax-17 1506	. 2 |- ( ps -> A. x ps )
2	1	19.23h 1478	1 |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Syntax hints:   -> wi 4   <-> wb 104   A.wal 1333   E.wex 1472

This theorem was proved from axioms:  ax-mp 5  ax-gen 1429  ax-ie2 1474  ax-17 1506

This theorem is referenced by:  19.23vv  1864  2eu4  2099  gencbval  2760  euind  2899  reuind  2917  unissb  3802  disjnim  3956  dftr2  4064  ssrelrel  4685  cotr  4966  dffun2  5179  fununi  5237  dff13  5715  acexmidlem2  5818