Theorem dedtOLD 1034

Description: Old version of dedt 1031. Obsolete as of 16-Mar-2021. (Contributed by NM, 26-Jun-2002.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

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

Assertion

Ref	Expression
dedtOLD	|- ( ch -> th )

Proof of Theorem dedtOLD

Step	Hyp	Ref	Expression
1		dedlema 1002	. 2 |- ( ch -> ( ph <-> ( ( ph /\ ch ) \/ ( ps /\ -. ch ) ) ) )
2		dedtOLD.2	. . 3 |- ta
3		dedtOLD.1	. . 3 |- ( ( ph <-> ( ( ph /\ ch ) \/ ( ps /\ -. ch ) ) ) -> ( th <-> ta ) )
4	2, 3	mpbiri 248	. 2 |- ( ( ph <-> ( ( ph /\ ch ) \/ ( ps /\ -. ch ) ) ) -> th )
5	1, 4	syl 17	1 |- ( ch -> th )

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