Theorem condcOLD 839

Description: Obsolete proof of condc 838 as of 18-Nov-2023. (Contributed by Jim Kingdon, 13-Mar-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
condcOLD	|- (DECID ph -> ( ( -. ph -> -. ps ) -> ( ps -> ph ) ) )

Proof of Theorem condcOLD

Step	Hyp	Ref	Expression
1		df-dc 820	. 2 |- (DECID ph <-> ( ph \/ -. ph ) )
2		ax-1 6	. . . 4 |- ( ph -> ( ps -> ph ) )
3	2	a1d 22	. . 3 |- ( ph -> ( ( -. ph -> -. ps ) -> ( ps -> ph ) ) )
4		pm2.27 40	. . . 4 |- ( -. ph -> ( ( -. ph -> -. ps ) -> -. ps ) )
5		ax-in2 604	. . . 4 |- ( -. ps -> ( ps -> ph ) )
6	4, 5	syl6 33	. . 3 |- ( -. ph -> ( ( -. ph -> -. ps ) -> ( ps -> ph ) ) )
7	3, 6	jaoi 705	. 2 |- ( ( ph \/ -. ph ) -> ( ( -. ph -> -. ps ) -> ( ps -> ph ) ) )
8	1, 7	sylbi 120	1 |- (DECID ph -> ( ( -. ph -> -. ps ) -> ( ps -> ph ) ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 697  DECID wdc 819

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 604  ax-io 698

This theorem depends on definitions:  df-bi 116  df-dc 820

This theorem is referenced by: (None)