Theorem 19.43OLD 1811

Description: Obsolete proof of 19.43 1810. Do not delete as it is referenced on the mmrecent.html page and in conventions-label 27259. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
19.43OLD	|- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )

Proof of Theorem 19.43OLD

Step	Hyp	Ref	Expression
1		ioran 511	. . . . 5 |- ( -. ( ph \/ ps ) <-> ( -. ph /\ -. ps ) )
2	1	albii 1747	. . . 4 |- ( A. x -. ( ph \/ ps ) <-> A. x ( -. ph /\ -. ps ) )
3		19.26 1798	. . . 4 |- ( A. x ( -. ph /\ -. ps ) <-> ( A. x -. ph /\ A. x -. ps ) )
4		alnex 1706	. . . . 5 |- ( A. x -. ph <-> -. E. x ph )
5		alnex 1706	. . . . 5 |- ( A. x -. ps <-> -. E. x ps )
6	4, 5	anbi12i 733	. . . 4 |- ( ( A. x -. ph /\ A. x -. ps ) <-> ( -. E. x ph /\ -. E. x ps ) )
7	2, 3, 6	3bitri 286	. . 3 |- ( A. x -. ( ph \/ ps ) <-> ( -. E. x ph /\ -. E. x ps ) )
8	7	notbii 310	. 2 |- ( -. A. x -. ( ph \/ ps ) <-> -. ( -. E. x ph /\ -. E. x ps ) )
9		df-ex 1705	. 2 |- ( E. x ( ph \/ ps ) <-> -. A. x -. ( ph \/ ps ) )
10		oran 517	. 2 |- ( ( E. x ph \/ E. x ps ) <-> -. ( -. E. x ph /\ -. E. x ps ) )
11	8, 9, 10	3bitr4i 292	1 |- ( E. x ( ph \/ ps ) <-> ( E. x ph \/ E. x ps ) )

Syntax hints:   -. wn 3   <-> wb 196   \/ wo 383   /\ 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-or 385  df-an 386  df-ex 1705

This theorem is referenced by: (None)