Theorem jaob 791

Description: Disjunction of antecedents. Compare Theorem *4.77 of [WhiteheadRussell] p. 121. (Contributed by NM, 30-May-1994.) (Proof shortened by Wolf Lammen, 9-Dec-2012.)

Assertion

Ref	Expression
jaob	|- ( ( ( ph \/ ch ) -> ps ) <-> ( ( ph -> ps ) /\ ( ch -> ps ) ) )

Proof of Theorem jaob

Step	Hyp	Ref	Expression
1		pm2.67-2 404	. . 3 |- ( ( ( ph \/ ch ) -> ps ) -> ( ph -> ps ) )
2		olc 386	. . . 4 |- ( ch -> ( ph \/ ch ) )
3	2	imim1i 60	. . 3 |- ( ( ( ph \/ ch ) -> ps ) -> ( ch -> ps ) )
4	1, 3	jca 535	. 2 |- ( ( ( ph \/ ch ) -> ps ) -> ( ( ph -> ps ) /\ ( ch -> ps ) ) )
5		pm3.44 514	. 2 |- ( ( ( ph -> ps ) /\ ( ch -> ps ) ) -> ( ( ph \/ ch ) -> ps ) )
6	4, 5	impbii 191	1 |- ( ( ( ph \/ ch ) -> ps ) <-> ( ( ph -> ps ) /\ ( ch -> ps ) ) )

Syntax hints:   -> wi 4   <-> wb 188   \/ wo 370   /\ wa 371

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 189  df-or 372  df-an 373

This theorem is referenced by:  pm4.77  795  pm5.53  804  pm4.83  939  axio  2420  unss  3607  ralunb  3614  intun  4266  intpr  4267  relop  4984  sqrt2irr  14294  algcvgblem  14529  efgred  17391  caucfil  22246  plydivex  23243  2sqlem6  24290  arg-ax  31069  tendoeq2  34335  ifpidg  36129