Theorem albid 1638

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 1542	. 2 |- ( ph -> A. x ph )
3		albid.2	. 2 |- ( ph -> ( ps <-> ch ) )
4	2, 3	albidh 1503	1 |- ( ph -> ( A. x ps <-> A. x ch ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1371   F/wnf 1483

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 1470  ax-gen 1472  ax-4 1533

This theorem depends on definitions:  df-bi 117  df-nf 1484

This theorem is referenced by:  alexdc  1642  19.32dc  1702  eubid  2061  ralbida  2500  ralbid2  2510  raleqf  2698  intab  3914  iotaexab  5251  bdsepnft  15860