Theorem 19.43OLD 1606

Description: Obsolete proof of 19.43 1605 as of 3-May-2016. Leave this in for the example on the mmrecent.html page. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem 19.43OLD

Step	Hyp	Ref	Expression
1		ioran 476	. . . . 5 |- (-. (ph \/ ps) <-> (-. ph /\ -. ps))
2	1	albii 1566	. . . 4 |- (A.x -. (ph \/ ps) <-> A.x(-. ph /\ -. ps))
3		19.26 1593	. . . 4 |- (A.x(-. ph /\ -. ps) <-> (A.x -. ph /\ A.x -. ps))
4		alnex 1543	. . . . 5 |- (A.x -. ph <-> -. E.xph)
5		alnex 1543	. . . . 5 |- (A.x -. ps <-> -. E.xps)
6	4, 5	anbi12i 678	. . . 4 |- ((A.x -. ph /\ A.x -. ps) <-> (-. E.xph /\ -. E.xps))
7	2, 3, 6	3bitri 262	. . 3 |- (A.x -. (ph \/ ps) <-> (-. E.xph /\ -. E.xps))
8	7	notbii 287	. 2 |- (-. A.x -. (ph \/ ps) <-> -. (-. E.xph /\ -. E.xps))
9		df-ex 1542	. 2 |- (E.x(ph \/ ps) <-> -. A.x -. (ph \/ ps))
10		oran 482	. 2 |- ((E.xph \/ E.xps) <-> -. (-. E.xph /\ -. E.xps))
11	8, 9, 10	3bitr4i 268	1 |- (E.x(ph \/ ps) <-> (E.xph \/ E.xps))

Syntax hints:  -. wn 3   <-> wb 176   \/ wo 357   /\ wa 358  A.wal 1540  E.wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-ex 1542

This theorem is referenced by: (None)