Theorem 19.21t 1605

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 1484	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		19.21ht 1604	. 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 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  ax-ial 1557  ax-i5r 1558

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

This theorem is referenced by:  19.21  1606  nfimd  1608  equs5or  1853  sbal1yz  2029  r19.21t  2581  ceqsalt  2798  sbciegft  3029