Theorem pm1.5 544

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 400	. . 3 |- ( ph -> ( ph \/ ch ) )
2	1	olcd 408	. 2 |- ( ph -> ( ps \/ ( ph \/ ch ) ) )
3		olc 399	. . 3 |- ( ch -> ( ph \/ ch ) )
4	3	orim2i 540	. 2 |- ( ( ps \/ ch ) -> ( ps \/ ( ph \/ ch ) ) )
5	2, 4	jaoi 394	1 |- ( ( ph \/ ( ps \/ ch ) ) -> ( ps \/ ( ph \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 383

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

This theorem is referenced by:  or12  545  meran1  32410  meran3  32412