Theorem albidh 1590

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

Hypotheses

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

Assertion

Ref	Expression
albidh	|- (ph -> (A.xps <-> A.xch))

Proof of Theorem albidh

Step	Hyp	Ref	Expression
1		albidh.1	. . 3 |- (ph -> A.xph)
2		albidh.2	. . 3 |- (ph -> (ps <-> ch))
3	1, 2	alrimih 1565	. 2 |- (ph -> A.x(ps <-> ch))
4		albi 1564	. 2 |- (A.x(ps <-> ch) -> (A.xps <-> A.xch))
5	3, 4	syl 15	1 |- (ph -> (A.xps <-> A.xch))

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

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  albidv  1625  albid  1772  ax10lem4  1941  ax9  1949  dral2  1966  dral2-o  2181  ax11indalem  2197  ax11inda2ALT  2198  ax11inda  2200