Theorem rblem1 1522

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
rblem1.1	|- (-. ph \/ ps)
rblem1.2	|- (-. ch \/ th)

Assertion

Ref	Expression
rblem1	|- (-. (ph \/ ch) \/ (ps \/ th))

Proof of Theorem rblem1

Step	Hyp	Ref	Expression
1		rblem1.2	. . 3 |- (-. ch \/ th)
2		rb-ax1 1517	. . 3 |- (-. (-. ch \/ th) \/ (-. (ps \/ ch) \/ (ps \/ th)))
3	1, 2	anmp 1516	. 2 |- (-. (ps \/ ch) \/ (ps \/ th))
4		rb-ax2 1518	. . 3 |- (-. (ch \/ ps) \/ (ps \/ ch))
5		rblem1.1	. . . . 5 |- (-. ph \/ ps)
6		rb-ax1 1517	. . . . 5 |- (-. (-. ph \/ ps) \/ (-. (ch \/ ph) \/ (ch \/ ps)))
7	5, 6	anmp 1516	. . . 4 |- (-. (ch \/ ph) \/ (ch \/ ps))
8		rb-ax2 1518	. . . 4 |- (-. (ph \/ ch) \/ (ch \/ ph))
9	7, 8	rbsyl 1521	. . 3 |- (-. (ph \/ ch) \/ (ch \/ ps))
10	4, 9	rbsyl 1521	. 2 |- (-. (ph \/ ch) \/ (ps \/ ch))
11	3, 10	rbsyl 1521	1 |- (-. (ph \/ ch) \/ (ps \/ th))

Syntax hints:  -. wn 3   \/ wo 357

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 177  df-or 359  df-an 360

This theorem is referenced by:  rblem4  1525  rblem5  1526  re2luk1  1530  re2luk2  1531