Theorem elimhOLD 1033

Description: Old version of elimh 1030. Obsolete as of 16-Mar-2021. (Contributed by NM, 26-Jun-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
elimhOLD.1	|- ( ( ph <-> ( ( ph /\ ch ) \/ ( ps /\ -. ch ) ) ) -> ( ch <-> ta ) )
elimhOLD.2	|- ( ( ps <-> ( ( ph /\ ch ) \/ ( ps /\ -. ch ) ) ) -> ( th <-> ta ) )
elimhOLD.3	|- th

Assertion

Ref	Expression
elimhOLD	|- ta

Proof of Theorem elimhOLD

Step	Hyp	Ref	Expression
1		dedlema 1002	. . . 4 |- ( ch -> ( ph <-> ( ( ph /\ ch ) \/ ( ps /\ -. ch ) ) ) )
2		elimhOLD.1	. . . 4 |- ( ( ph <-> ( ( ph /\ ch ) \/ ( ps /\ -. ch ) ) ) -> ( ch <-> ta ) )
3	1, 2	syl 17	. . 3 |- ( ch -> ( ch <-> ta ) )
4	3	ibi 256	. 2 |- ( ch -> ta )
5		elimhOLD.3	. . 3 |- th
6		dedlemb 1003	. . . 4 |- ( -. ch -> ( ps <-> ( ( ph /\ ch ) \/ ( ps /\ -. ch ) ) ) )
7		elimhOLD.2	. . . 4 |- ( ( ps <-> ( ( ph /\ ch ) \/ ( ps /\ -. ch ) ) ) -> ( th <-> ta ) )
8	6, 7	syl 17	. . 3 |- ( -. ch -> ( th <-> ta ) )
9	5, 8	mpbii 223	. 2 |- ( -. ch -> ta )
10	4, 9	pm2.61i 176	1 |- ta

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383   /\ wa 384

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

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386

This theorem is referenced by:  con3OLD  1035