Theorem rbsyl 1681

Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 18-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
rbsyl.1	|- ( -. ps \/ ch )
rbsyl.2	|- ( ph \/ ps )

Assertion

Ref	Expression
rbsyl	|- ( ph \/ ch )

Proof of Theorem rbsyl

Step	Hyp	Ref	Expression
1		rbsyl.2	. 2 |- ( ph \/ ps )
2		rbsyl.1	. . 3 |- ( -. ps \/ ch )
3		rb-ax1 1677	. . 3 |- ( -. ( -. ps \/ ch ) \/ ( -. ( ph \/ ps ) \/ ( ph \/ ch ) ) )
4	2, 3	anmp 1676	. 2 |- ( -. ( ph \/ ps ) \/ ( ph \/ ch ) )
5	1, 4	anmp 1676	1 |- ( ph \/ ch )

Syntax hints:   -. wn 3   \/ 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  df-an 386

This theorem is referenced by:  rblem1  1682  rblem2  1683  rblem3  1684  rblem4  1685  rblem5  1686  rblem6  1687  re2luk1  1690  re2luk2  1691  re2luk3  1692