rblem1 - Metamath Proof Explorer

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Theorem rblem1 1682

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	$\/$
rblem1.2	$\/$

**Assertion**
Ref	Expression
rblem1	$\/$ $\/$ $\/$

**Proof of Theorem rblem1**
Step	Hyp	Ref	Expression
1		rblem1.2	. . 3 $\/$
2		rb-ax1 1677	. . 3 $\/$ $\/$ $\/$ $\/$ $\/$
3	1, 2	anmp 1676	. 2 $\/$ $\/$ $\/$
4		rb-ax2 1678	. . 3 $\/$ $\/$ $\/$
5		rblem1.1	. . . . 5 $\/$
6		rb-ax1 1677	. . . . 5 $\/$ $\/$ $\/$ $\/$ $\/$
7	5, 6	anmp 1676	. . . 4 $\/$ $\/$ $\/$
8		rb-ax2 1678	. . . 4 $\/$ $\/$ $\/$
9	7, 8	rbsyl 1681	. . 3 $\/$ $\/$ $\/$
10	4, 9	rbsyl 1681	. 2 $\/$ $\/$ $\/$
11	3, 10	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: rblem4 1685 rblem5 1686 re2luk1 1690 re2luk2 1691

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