Theorem 19.23v 1811

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 1464	. 2 |- ( ps -> A. x ps )
2	1	19.23h 1432	1 |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Syntax hints:   -> wi 4   <-> wb 103   A.wal 1287   E.wex 1426

This theorem was proved from axioms:  ax-mp 7  ax-gen 1383  ax-ie2 1428  ax-17 1464

This theorem is referenced by:  19.23vv  1812  2eu4  2041  gencbval  2667  euind  2802  reuind  2820  unissb  3683  disjnim  3836  dftr2  3938  ssrelrel  4538  cotr  4813  dffun2  5025  fununi  5082  dff13  5547  acexmidlem2  5649