Theorem pm2.1dc 745

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 743	. . 3 |- (DECID ph <-> ( ph \/ -. ph ) )
2		orcom 647	. . 3 |- ( ( ph \/ -. ph ) <-> ( -. ph \/ ph ) )
3	1, 2	bitri 173	. 2 |- (DECID ph <-> ( -. ph \/ ph ) )
4	3	biimpi 113	1 |- (DECID ph -> ( -. ph \/ ph ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 629  DECID wdc 742

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630

This theorem depends on definitions:  df-bi 110  df-dc 743

This theorem is referenced by:  pm2.6dc  759  rabrsndc  3438