re2luk3 - Metamath Proof Explorer

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Theorem re2luk3 1692

Description: luk-3 1582 derived from Russell-Bernays'.

This theorem, along with re1axmp 1689, re2luk1 1690, and re2luk2 1691 shows that rb-ax1 1677, rb-ax2 1678, rb-ax3 1679, and rb-ax4 1680, along with anmp 1676, can be used as a complete axiomatization of propositional calculus. (Contributed by Anthony Hart, 19-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

**Assertion**
Ref	Expression
re2luk3

**Proof of Theorem re2luk3**
Step	Hyp	Ref	Expression
1		rb-imdf 1675	. . . 4 $\/$ $\/$ $\/$ $\/$ $\/$
2	1	rblem7 1688	. . 3 $\/$ $\/$
3		rb-ax4 1680	. . . . . 6 $\/$ $\/$
4		rb-ax3 1679	. . . . . 6 $\/$ $\/$
5	3, 4	rbsyl 1681	. . . . 5 $\/$
6		rb-ax2 1678	. . . . 5 $\/$ $\/$ $\/$
7	5, 6	anmp 1676	. . . 4 $\/$
8		rblem2 1683	. . . 4 $\/$ $\/$ $\/$ $\/$
9	7, 8	anmp 1676	. . 3 $\/$ $\/$
10	2, 9	rbsyl 1681	. 2 $\/$
11		rb-imdf 1675	. . 3 $\/$ $\/$ $\/$ $\/$ $\/$
12	11	rblem7 1688	. 2 $\/$ $\/$
13	10, 12	anmp 1676	1

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4 $\/$ 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: (None)

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