Theorem 19.23v 1907

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 1550	. 2 |- ( ps -> A. x ps )
2	1	19.23h 1522	1 |- ( A. x ( ph -> ps ) <-> ( E. x ph -> ps ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1371   E.wex 1516

This theorem was proved from axioms:  ax-mp 5  ax-gen 1473  ax-ie2 1518  ax-17 1550

This theorem is referenced by:  19.23vv  1908  2eu4  2149  gencbval  2826  euind  2967  reuind  2985  snssb  3777  unissb  3894  disjnim  4049  dftr2  4160  ssrelrel  4793  cotr  5083  dffun2  5300  fununi  5361  dff13  5860  acexmidlem2  5964