Theorem albid 1626

Description: Formula-building rule for universal quantifier (deduction form). (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 1530	. 2 |- ( ph -> A. x ph )
3		albid.2	. 2 |- ( ph -> ( ps <-> ch ) )
4	2, 3	albidh 1491	1 |- ( ph -> ( A. x ps <-> A. x ch ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1362   F/wnf 1471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-4 1521

This theorem depends on definitions:  df-bi 117  df-nf 1472

This theorem is referenced by:  alexdc  1630  19.32dc  1690  eubid  2049  ralbida  2488  ralbid2  2498  raleqf  2686  intab  3899  iotaexab  5233  bdsepnft  15384