Theorem albidh 1456

Description: Formula-building rule for universal quantifier (deduction form). (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 1445	. 2 |- ( ph -> A. x ( ps <-> ch ) )
4		albi 1444	. 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 104   A.wal 1329

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  nfbidf  1519  albid  1594  dral2  1709  ax11v2  1792  albidv  1796  equs5or  1802  sbal2  1997  eubidh  2005