Theorem 19.23v 1763

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 1419	. 2 |- ( ps -> A. x ps )
2	1	19.23h 1387	1 |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Syntax hints:   -> wi 4   <-> wb 98   A.wal 1241   E.wex 1381

This theorem was proved from axioms:  ax-mp 7  ax-gen 1338  ax-ie2 1383  ax-17 1419

This theorem is referenced by:  19.23vv  1764  2eu4  1993  gencbval  2602  euind  2728  reuind  2744  unissb  3610  dftr2  3856  ssrelrel  4440  cotr  4706  dffun2  4912  fununi  4967  dff13  5407  acexmidlem2  5509