Theorem pm1.5 529

Description: Axiom *1.5 (Assoc) of [WhiteheadRussell] p. 96. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm1.5	|- ( ( ph \/ ( ps \/ ch ) ) -> ( ps \/ ( ph \/ ch ) ) )

Proof of Theorem pm1.5

Step	Hyp	Ref	Expression
1		orc 391	. . 3 |- ( ph -> ( ph \/ ch ) )
2	1	olcd 399	. 2 |- ( ph -> ( ps \/ ( ph \/ ch ) ) )
3		olc 390	. . 3 |- ( ch -> ( ph \/ ch ) )
4	3	orim2i 525	. 2 |- ( ( ps \/ ch ) -> ( ps \/ ( ph \/ ch ) ) )
5	2, 4	jaoi 385	1 |- ( ( ph \/ ( ps \/ ch ) ) -> ( ps \/ ( ph \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 374

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 190  df-or 376

This theorem is referenced by:  or12  530  meran1  31119  meran3  31121