Theorem albidh 1793

Description: Formula-building rule for universal quantifier (deduction rule). (Contributed by NM, 26-May-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 1751	. 2 |- ( ph -> A. x ( ps <-> ch ) )
4		albi 1746	. 2 |- ( A. x ( ps <-> ch ) -> ( A. x ps <-> A. x ch ) )
5	3, 4	syl 17	1 |- ( ph -> ( A. x ps <-> A. x ch ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197

This theorem is referenced by:  albidv  1849  albid  2090  albidOLD  2199  dral2-o  34215  ax12indalem  34230  ax12inda2ALT  34231  ax12inda  34233