re2luk2 - Metamath Proof Explorer

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Theorem re2luk2 1691

Description: luk-2 1581 derived from Russell-Bernays'. (Contributed by Anthony Hart, 19-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

**Assertion**
Ref	Expression
re2luk2

**Proof of Theorem re2luk2**
Step	Hyp	Ref	Expression
1		rb-ax4 1680	. . . 4 $\/$ $\/$
2		rb-ax3 1679	. . . . . . 7 $\/$ $\/$
3	1, 2	rbsyl 1681	. . . . . 6 $\/$
4		rb-ax4 1680	. . . . . . . . 9 $\/$ $\/$
5		rb-ax3 1679	. . . . . . . . 9 $\/$ $\/$
6	4, 5	rbsyl 1681	. . . . . . . 8 $\/$
7		rb-ax2 1678	. . . . . . . 8 $\/$ $\/$ $\/$
8	6, 7	anmp 1676	. . . . . . 7 $\/$
9	8, 3	rblem1 1682	. . . . . 6 $\/$ $\/$ $\/$
10	3, 9	anmp 1676	. . . . 5 $\/$
11	10, 3	rblem1 1682	. . . 4 $\/$ $\/$ $\/$
12	1, 11	rbsyl 1681	. . 3 $\/$ $\/$
13		rb-imdf 1675	. . . 4 $\/$ $\/$ $\/$ $\/$ $\/$
14	13	rblem6 1687	. . 3 $\/$ $\/$
15	12, 14	rbsyl 1681	. 2 $\/$
16		rb-imdf 1675	. . 3 $\/$ $\/$ $\/$ $\/$ $\/$
17	16	rblem7 1688	. 2 $\/$ $\/$
18	15, 17	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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