Theorem 4exbidv 1630

Description: Formula-building rule for 4 existential quantifiers (deduction rule). (Contributed by NM, 3-Aug-1995.)

Hypothesis

Ref	Expression
4exbidv.1	|- (ph -> (ps <-> ch))

Assertion

Ref	Expression
4exbidv	|- (ph -> (E.xE.yE.zE.wps <-> E.xE.yE.zE.wch))

Distinct variable groups:   ph,x   ph,y   ph,z   ph,w

Allowed substitution hints:   ps(x,y,z,w)   ch(x,y,z,w)

Proof of Theorem 4exbidv

Step	Hyp	Ref	Expression
1		4exbidv.1	. . 3 |- (ph -> (ps <-> ch))
2	1	2exbidv 1628	. 2 |- (ph -> (E.zE.wps <-> E.zE.wch))
3	2	2exbidv 1628	1 |- (ph -> (E.xE.yE.zE.wps <-> E.xE.yE.zE.wch))

Syntax hints:   -> wi 4   <-> wb 176  E.wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  ceqsex8v  2901  opbrop  4842  ov3  5600