Theorem 19.42vv 968

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 group(s):   ph,x   ph,y

Proof of Theorem 19.42vv

Step	Hyp	Ref	Expression
1		exdistr 967	. 2 |- (E.xE.y(ph /\ ps) <-> E.x(ph /\ E.yps))
2		19.42v 966	. 2 |- (E.x(ph /\ E.yps) <-> (ph /\ E.xE.yps))
3	1, 2	bitr 151	1 |- (E.xE.y(ph /\ ps) <-> (ph /\ E.xE.yps))

Syntax hints:   <-> wb 127   /\ wa 196  E.wex 678

This theorem is referenced by:  exdistr2 969  eeeanv 981  dfoprab2 3021  oprabex3 3046  oprabval3 3052  xpassen 3344  distrlem1pr 3921  distrlem5pr 3925

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-17 925

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679

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