Theorem 19.23v 1906

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 1549	. 2 |- ( ps -> A. x ps )
2	1	19.23h 1521	1 |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1371   E.wex 1515

This theorem was proved from axioms:  ax-mp 5  ax-gen 1472  ax-ie2 1517  ax-17 1549

This theorem is referenced by:  19.23vv  1907  2eu4  2147  gencbval  2821  euind  2960  reuind  2978  snssb  3766  unissb  3880  disjnim  4035  dftr2  4144  ssrelrel  4775  cotr  5064  dffun2  5281  fununi  5342  dff13  5837  acexmidlem2  5941