Theorem 19.42vv 1308

Description: Theorem 19.42 of [Margaris] p. 90 with 2 quantifiers.

Assertion

Ref	Expression
19.42vv	|- (E.xE.y(ph /\ ps) <-> (ph /\ E.xE.yps))

Distinct variable groups:   ph,x   ph,y

Proof of Theorem 19.42vv

Step	Hyp	Ref	Expression
1		exdistr 1307	. 2 |- (E.xE.y(ph /\ ps) <-> E.x(ph /\ E.yps))
2		19.42v 1306	. 2 |- (E.x(ph /\ E.yps) <-> (ph /\ E.xE.yps))
3	1, 2	bitr 173	1 |- (E.xE.y(ph /\ ps) <-> (ph /\ E.xE.yps))

Syntax hints:   <-> wb 146   /\ wa 223  E.wex 978

This theorem is referenced by:  exdistr2 1309  eeeanv 1322  dfoprab2 3982  resoprab 4000  oprabex3 4013  oprabval3 4021  oprabval6g 4023  xpassen 4427  distrlem1pr 5107  distrlem5pr 5111  axaddopr 5245  axmulopr 5246

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 979

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