rblem5 - Metamath Proof Explorer

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Theorem rblem5 1686

Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 19-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

**Assertion**
Ref	Expression
rblem5	$\/$ $\/$ $\/$

**Proof of Theorem rblem5**
Step	Hyp	Ref	Expression
1		rb-ax2 1678	. 2 $\/$ $\/$ $\/$
2		rb-ax4 1680	. . . . 5 $\/$ $\/$
3		rb-ax3 1679	. . . . 5 $\/$ $\/$
4	2, 3	rbsyl 1681	. . . 4 $\/$
5		rb-ax4 1680	. . . . . . 7 $\/$ $\/$
6		rb-ax3 1679	. . . . . . 7 $\/$ $\/$
7	5, 6	rbsyl 1681	. . . . . 6 $\/$
8		rb-ax2 1678	. . . . . 6 $\/$ $\/$ $\/$
9	7, 8	anmp 1676	. . . . 5 $\/$
10	9, 4	rblem1 1682	. . . 4 $\/$ $\/$ $\/$
11	4, 10	anmp 1676	. . 3 $\/$
12		rb-ax4 1680	. . . . 5 $\/$ $\/$
13		rb-ax3 1679	. . . . 5 $\/$ $\/$
14	12, 13	rbsyl 1681	. . . 4 $\/$
15		rb-ax2 1678	. . . 4 $\/$ $\/$ $\/$
16	14, 15	anmp 1676	. . 3 $\/$
17	11, 16	rblem1 1682	. 2 $\/$ $\/$ $\/$
18	1, 17	rbsyl 1681	1 $\/$ $\/$ $\/$

Colors of variables: wff setvar class

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: rblem6 1687 rblem7 1688

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