Theorem 19.21t 1582

Description: Closed form of Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 27-May-1997.)

Assertion

Ref	Expression
19.21t	|- ( F/ x ph -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )

Proof of Theorem 19.21t

Step	Hyp	Ref	Expression
1		df-nf 1461	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		19.21ht 1581	. 2 |- ( A. x ( ph -> A. x ph ) -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )
3	1, 2	sylbi 121	1 |- ( F/ x ph -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1351   F/wnf 1460

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 1447  ax-gen 1449  ax-4 1510  ax-ial 1534  ax-i5r 1535

This theorem depends on definitions:  df-bi 117  df-nf 1461

This theorem is referenced by:  19.21  1583  nfimd  1585  equs5or  1830  sbal1yz  2001  r19.21t  2552  ceqsalt  2764  sbciegft  2994