Theorem 2albidv 1278

Description: Formula-building rule for 2 existential quantifiers (deduction rule).

Hypothesis

Ref	Expression
2albidv.1	|- (ph -> (ps <-> ch))

Assertion

Ref	Expression
2albidv	|- (ph -> (A.xA.yps <-> A.xA.ych))

Distinct variable groups:   ph,x   ph,y

Proof of Theorem 2albidv

Step	Hyp	Ref	Expression
1		2albidv.1	. . 3 |- (ph -> (ps <-> ch))
2	1	albidv 1276	. 2 |- (ph -> (A.yps <-> A.ych))
3	2	albidv 1276	1 |- (ph -> (A.xA.yps <-> A.xA.ych))

Syntax hints:   -> wi 3   <-> wb 146  A.wal 952

This theorem is referenced by:  2mo 1445  2eu6 1452  f1fv 3865  closedsub 9032  isfil 10469

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-17 969  ax-4 971  ax-5o 973

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

Copyright terms: Public domain