Theorem bi2aldv 937

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

Hypothesis

Ref	Expression
bi2aldv.1	|- (ph -> (ps <-> ch))

Assertion

Ref	Expression
bi2aldv	|- (ph -> (A.xA.yps <-> A.xA.ych))

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

Proof of Theorem bi2aldv

Step	Hyp	Ref	Expression
1		bi2aldv.1	. . 3 |- (ph -> (ps <-> ch))
2	1	bialdv 935	. 2 |- (ph -> (A.yps <-> A.ych))
3	2	bialdv 935	1 |- (ph -> (A.xA.yps <-> A.xA.ych))

Syntax hints:   -> wi 2   <-> wb 127  A.wal 672

This theorem is referenced by:  f1fv 2916  closedsub 5128

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

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