Theorem bi4exdv 940

Description: Formula-building rule for 4 existential quantifiers (deduction rule).

Hypothesis

Ref	Expression
bi4exdv.1	|- (ph -> (ps <-> ch))

Assertion

Ref	Expression
bi4exdv	|- (ph -> (E.xE.yE.zE.wps <-> E.xE.yE.zE.wch))

Distinct variable group(s):   ph,x   ph,y   ph,z   ph,w

Proof of Theorem bi4exdv

Step	Hyp	Ref	Expression
1		bi4exdv.1	. . 3 |- (ph -> (ps <-> ch))
2	1	bi2exdv 938	. 2 |- (ph -> (E.zE.wps <-> E.zE.wch))
3	2	bi2exdv 938	1 |- (ph -> (E.xE.yE.zE.wps <-> E.xE.yE.zE.wch))

Syntax hints:   -> wi 2   <-> wb 127  E.wex 678

This theorem is referenced by:  copsex4g 1904  opbrop 2472  oprabval3 3052  brecop 3242  th3q 3253

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-gen 677  ax-17 925

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

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