Theorem albidh 1369

Description: Formula-building rule for universal quantifier (deduction rule). (Contributed by NM, 5-Aug-1993.)

Hypotheses

Ref	Expression
albidh.1	|- ( ph -> A. x ph )
albidh.2	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
albidh	|- ( ph -> ( A. x ps <-> A. x ch ) )

Proof of Theorem albidh

Step	Hyp	Ref	Expression
1		albidh.1	. . 3 |- ( ph -> A. x ph )
2		albidh.2	. . 3 |- ( ph -> ( ps <-> ch ) )
3	1, 2	alrimih 1358	. 2 |- ( ph -> A. x ( ps <-> ch ) )
4		albi 1357	. 2 |- ( A. x ( ps <-> ch ) -> ( A. x ps <-> A. x ch ) )
5	3, 4	syl 14	1 |- ( ph -> ( A. x ps <-> A. x ch ) )

Syntax hints:   -> wi 4   <-> wb 98   A.wal 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  nfbidf  1432  albid  1506  dral2  1619  ax11v2  1701  albidv  1705  equs5or  1711  sbal2  1898  eubidh  1906