rblem3 - Metamath Proof Explorer

	Metamath Proof Explorer		< Previous Next > Nearby theorems
Mirrors > Home > MPE Home > Th. List > rblem3		Structured version Visualization version Unicode version

Theorem rblem3 1684

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.)

**Assertion**
Ref	Expression
rblem3	$\/$ $\/$ $\/$ $\/$

**Proof of Theorem rblem3**
Step	Hyp	Ref	Expression
1		rb-ax2 1678	. 2 $\/$ $\/$ $\/$ $\/$ $\/$
2		rblem2 1683	. . 3 $\/$ $\/$ $\/$ $\/$
3		rb-ax2 1678	. . 3 $\/$ $\/$ $\/$
4	2, 3	rbsyl 1681	. 2 $\/$ $\/$ $\/$ $\/$
5	1, 4	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

W3C validator