Theorem 2albidv 1627

Description: Formula-building rule for 2 universal quantifiers (deduction rule). (Contributed by NM, 4-Mar-1997.)

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

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

Proof of Theorem 2albidv

Step	Hyp	Ref	Expression
1		2albidv.1	. . 3 |- (ph -> (ps <-> ch))
2	1	albidv 1625	. 2 |- (ph -> (A.yps <-> A.ych))
3	2	albidv 1625	1 |- (ph -> (A.xA.yps <-> A.xA.ych))

Syntax hints:   -> wi 4   <-> wb 176  A.wal 1540

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

This theorem is referenced by:  2mo  2282  2eu6  2289  nnsucelr  4428  ssfin  4470  ncfinlower  4483  dff13  5471  fnfrec  6320