Theorem albid 1546

Description: Formula-building rule for universal quantifier (deduction rule). (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
albid.1	|- F/ x ph
albid.2	|- ( ph -> ( ps <-> ch ) )

Assertion

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

Proof of Theorem albid

Step	Hyp	Ref	Expression
1		albid.1	. . 3 |- F/ x ph
2	1	nfri 1452	. 2 |- ( ph -> A. x ph )
3		albid.2	. 2 |- ( ph -> ( ps <-> ch ) )
4	2, 3	albidh 1409	1 |- ( ph -> ( A. x ps <-> A. x ch ) )

Syntax hints:   -> wi 4   <-> wb 103   A.wal 1282   F/wnf 1389

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-4 1440

This theorem depends on definitions:  df-bi 115  df-nf 1390

This theorem is referenced by:  alexdc  1550  19.32dc  1609  eubid  1948  ralbida  2362  raleqf  2545  intab  3665  bdsepnft  10678  strcollnft  10779  sscoll2  10783