Theorem pm2.521gdc 853

Description: A general instance of Theorem *2.521 of [WhiteheadRussell] p. 107, under a decidability condition. (Contributed by BJ, 28-Oct-2023.)

Assertion

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

Proof of Theorem pm2.521gdc

Step	Hyp	Ref	Expression
1		pm2.5gdc 851	. 2 |- (DECID ph -> ( -. ( ph -> ps ) -> ( -. ph -> -. ch ) ) )
2		condc 838	. 2 |- (DECID ph -> ( ( -. ph -> -. ch ) -> ( ch -> ph ) ) )
3	1, 2	syld 45	1 |- (DECID ph -> ( -. ( ph -> ps ) -> ( ch -> ph ) ) )

Syntax hints:   -. wn 3   -> wi 4  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-in1 603  ax-in2 604  ax-io 698

This theorem depends on definitions:  df-bi 116  df-stab 816  df-dc 820

This theorem is referenced by:  pm2.521dc  854