Theorem 3exbidv 1282

Description: Formula-building rule for 3 existential quantifiers (deduction rule).

Hypothesis

Ref	Expression
3exbidv.1	|- (ph -> (ps <-> ch))

Assertion

Ref	Expression
3exbidv	|- (ph -> (E.xE.yE.zps <-> E.xE.yE.zch))

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

Proof of Theorem 3exbidv

Step	Hyp	Ref	Expression
1		3exbidv.1	. . 3 |- (ph -> (ps <-> ch))
2	1	exbidv 1279	. 2 |- (ph -> (E.zps <-> E.zch))
3	2	2exbidv 1281	1 |- (ph -> (E.xE.yE.zps <-> E.xE.yE.zch))

Syntax hints:   -> wi 3   <-> wb 146  E.wex 980

This theorem is referenced by:  eloprabg 4007

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-17 971  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

Copyright terms: Public domain