Theorem pm2.521dc 797

Description: Theorem *2.521 of [WhiteheadRussell] p. 107, but with an additional decidability condition. (Contributed by Jim Kingdon, 5-May-2018.)

Assertion

Ref	Expression
pm2.521dc	|- (DECID ph -> ( -. ( ph -> ps ) -> ( ps -> ph ) ) )

Proof of Theorem pm2.521dc

Step	Hyp	Ref	Expression
1		pm2.52 614	. 2 |- ( -. ( ph -> ps ) -> ( -. ph -> -. ps ) )
2		condc 782	. 2 |- (DECID ph -> ( ( -. ph -> -. ps ) -> ( ps -> ph ) ) )
3	1, 2	syl5 32	1 |- (DECID ph -> ( -. ( ph -> ps ) -> ( ps -> ph ) ) )

Syntax hints:   -. wn 3   -> wi 4  DECID wdc 775

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 577  ax-io 662

This theorem depends on definitions:  df-bi 115  df-dc 776

This theorem is referenced by: (None)