Theorem 19.21t 1561

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 1437	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		19.21ht 1560	. 2 |- ( A. x ( ph -> A. x ph ) -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )
3	1, 2	sylbi 120	1 |- ( F/ x ph -> ( A. x ( ph -> ps ) <-> ( ph -> A. x ps ) ) )

Syntax hints:   -> wi 4   <-> wb 104   A.wal 1329   F/wnf 1436

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-5 1423  ax-gen 1425  ax-4 1487  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1437

This theorem is referenced by:  19.21  1562  nfimd  1564  equs5or  1802  sbal1yz  1976  r19.21t  2507  ceqsalt  2712  sbciegft  2939