Theorem 19.21t 1519

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 1395	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		19.21ht 1518	. 2 |- ( A. x ( ph -> A. x ph ) -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )
3	1, 2	sylbi 119	1 |- ( F/ x ph -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )

Syntax hints:   -> wi 4   <-> wb 103   A.wal 1287   F/wnf 1394

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 1381  ax-gen 1383  ax-4 1445  ax-ial 1472  ax-i5r 1473

This theorem depends on definitions:  df-bi 115  df-nf 1395

This theorem is referenced by:  19.21  1520  nfimd  1522  equs5or  1758  sbal1yz  1925  r19.21t  2448  ceqsalt  2645  sbciegft  2869