Theorem 19.41vvv 965

Description: Theorem 19.41 of [Margaris] p. 90 with 3 quantifiers.

Assertion

Ref	Expression
19.41vvv	|- (E.xE.yE.z(ph /\ ps) <-> (E.xE.yE.zph /\ ps))

Distinct variable group(s):   ps,x   ps,y   ps,z

Proof of Theorem 19.41vvv

Step	Hyp	Ref	Expression
1		19.41vv 964	. . 3 |- (E.yE.z(ph /\ ps) <-> (E.yE.zph /\ ps))
2	1	biex 733	. 2 |- (E.xE.yE.z(ph /\ ps) <-> E.x(E.yE.zph /\ ps))
3		19.41v 963	. 2 |- (E.x(E.yE.zph /\ ps) <-> (E.xE.yE.zph /\ ps))
4	2, 3	bitr 151	1 |- (E.xE.yE.z(ph /\ ps) <-> (E.xE.yE.zph /\ ps))

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

This theorem is referenced by:  eloprabg 3035

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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