Theorem pm2.1dc 822

Description: Commuted law of the excluded middle for a decidable proposition. Based on theorem *2.1 of [WhiteheadRussell] p. 101. (Contributed by Jim Kingdon, 25-Mar-2018.)

Assertion

Ref	Expression
pm2.1dc	|- (DECID ph -> ( -. ph \/ ph ) )

Proof of Theorem pm2.1dc

Step	Hyp	Ref	Expression
1		df-dc 820	. . 3 |- (DECID ph <-> ( ph \/ -. ph ) )
2		orcom 717	. . 3 |- ( ( ph \/ -. ph ) <-> ( -. ph \/ ph ) )
3	1, 2	bitri 183	. 2 |- (DECID ph <-> ( -. ph \/ ph ) )
4	3	biimpi 119	1 |- (DECID ph -> ( -. ph \/ 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-io 698

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

This theorem is referenced by:  pm2.6dc  847  rabrsndc  3591