rblem6 - Metamath Proof Explorer

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Theorem rblem6 1687

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.)

**Hypothesis**
Ref	Expression
rblem6.1	$\/$ $\/$ $\/$

**Assertion**
Ref	Expression
rblem6	$\/$

**Proof of Theorem rblem6**
Step	Hyp	Ref	Expression
1		rblem6.1	. 2 $\/$ $\/$ $\/$
2		rb-ax4 1680	. . . . . . 7 $\/$ $\/$ $\/$ $\/$ $\/$
3		rb-ax3 1679	. . . . . . 7 $\/$ $\/$ $\/$ $\/$ $\/$
4	2, 3	rbsyl 1681	. . . . . 6 $\/$ $\/$ $\/$
5		rb-ax2 1678	. . . . . 6 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
6	4, 5	anmp 1676	. . . . 5 $\/$ $\/$ $\/$
7		rblem3 1684	. . . . 5 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
8	6, 7	anmp 1676	. . . 4 $\/$ $\/$ $\/$ $\/$ $\/$
9		rb-ax2 1678	. . . 4 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
10	8, 9	anmp 1676	. . 3 $\/$ $\/$ $\/$ $\/$ $\/$
11		rblem5 1686	. . 3 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
12	10, 11	anmp 1676	. 2 $\/$ $\/$ $\/$ $\/$ $\/$
13	1, 12	anmp 1676	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: re1axmp 1689 re2luk1 1690 re2luk2 1691

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