Theorem 19.3 1547

Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)

Hypothesis

Ref	Expression
19.3.1	|- F/ x ph

Assertion

Ref	Expression
19.3	|- ( A. x ph <-> ph )

Proof of Theorem 19.3

Step	Hyp	Ref	Expression
1		sp 1504	. 2 |- ( A. x ph -> ph )
2		19.3.1	. . 3 |- F/ x ph
3	2	nfri 1512	. 2 |- ( ph -> A. x ph )
4	1, 3	impbii 125	1 |- ( A. x ph <-> ph )

Syntax hints:   <-> wb 104   A.wal 1346   F/wnf 1453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-4 1503

This theorem depends on definitions:  df-bi 116  df-nf 1454

This theorem is referenced by:  19.16  1548  19.17  1549  19.27  1554  19.28  1556  19.37-1  1667  rexxfrd  4448