Theorem alinexa 1770

Description: A transformation of quantifiers and logical connectives. (Contributed by NM, 19-Aug-1993.)

Assertion

Ref	Expression
alinexa	|- ( A. x ( ph -> -. ps ) <-> -. E. x ( ph /\ ps ) )

Proof of Theorem alinexa

Step	Hyp	Ref	Expression
1		imnang 1769	. 2 |- ( A. x ( ph -> -. ps ) <-> A. x -. ( ph /\ ps ) )
2		alnex 1706	. 2 |- ( A. x -. ( ph /\ ps ) <-> -. E. x ( ph /\ ps ) )
3	1, 2	bitri 264	1 |- ( A. x ( ph -> -. ps ) <-> -. E. x ( ph /\ ps ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   /\ wa 384   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  equs3  1875  ralnexOLD  2993  r2exlem  3059  zfregs2  8609  ac6n  9307  nnunb  11288  alexsubALTlem3  21853  nmobndseqi  27634  bj-exnalimn  32610  bj-ssbn  32641  frege124d  38053  zfregs2VD  39076