Theorem pm5.6 951

Description: Conjunction in antecedent versus disjunction in consequent. Theorem *5.6 of [WhiteheadRussell] p. 125. (Contributed by NM, 8-Jun-1994.)

Assertion

Ref	Expression
pm5.6	|- ( ( ( ph /\ -. ps ) -> ch ) <-> ( ph -> ( ps \/ ch ) ) )

Proof of Theorem pm5.6

Step	Hyp	Ref	Expression
1		impexp 462	. 2 |- ( ( ( ph /\ -. ps ) -> ch ) <-> ( ph -> ( -. ps -> ch ) ) )
2		df-or 385	. . 3 |- ( ( ps \/ ch ) <-> ( -. ps -> ch ) )
3	2	imbi2i 326	. 2 |- ( ( ph -> ( ps \/ ch ) ) <-> ( ph -> ( -. ps -> ch ) ) )
4	1, 3	bitr4i 267	1 |- ( ( ( ph /\ -. ps ) -> ch ) <-> ( ph -> ( ps \/ ch ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386

This theorem is referenced by:  ssundif  4052  brdom3  9350  grothprim  9656  eliccelico  29539  elicoelioo  29540  ballotlemfc0  30554  ballotlemfcc  30555  elicc3  32311  ifpidg  37836  icccncfext  40100