Theorem 19.23v 1883

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 1526	. 2 |- ( ps -> A. x ps )
2	1	19.23h 1498	1 |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1351   E.wex 1492

This theorem was proved from axioms:  ax-mp 5  ax-gen 1449  ax-ie2 1494  ax-17 1526

This theorem is referenced by:  19.23vv  1884  2eu4  2119  gencbval  2785  euind  2924  reuind  2942  snssb  3725  unissb  3839  disjnim  3994  dftr2  4103  ssrelrel  4726  cotr  5010  dffun2  5226  fununi  5284  dff13  5768  acexmidlem2  5871