kmlem7 - Metamath Proof Explorer

Metamath Proof Explorer

< Previous Next >
Related theorems
Unicode version

Theorem kmlem7 4771

Description: Lemma for 5-quantifier AC of Kurt Maes, Th. 4, part of 4 => 1.

**Assertion**
Ref	Expression
kmlem7	$/\$ $/\$

**Proof of Theorem kmlem7**
Step	Hyp	Ref	Expression
1		kmlem6 4770	. 2 $/\$
2		ralinexa 1683	. . . . . 6 $/\$
3	2	rexbii 1668	. . . . 5 $/\$
4		rexnal 1654	. . . . 5 $/\$ $/\$
5	3, 4	bitr 173	. . . 4 $/\$
6	5	ralbii 1667	. . 3 $/\$
7		ralnex 1653	. . 3 $/\$ $/\$
8	6, 7	bitr 173	. 2 $/\$
9	1, 8	sylib 198	1 $/\$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 2

wi 3 $/\$ wa 223

wceq 956

wcel 958

wne 1585

wral 1645

wrex 1646

cin 2046

c0 2280

This theorem is referenced by: kmlem13 4777

This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 962 ax-gen 963 ax-8 964 ax-10 966 ax-12 968 ax-17 971 ax-4 973 ax-5o 975 ax-6o 978 ax-9o 1123 ax-10o 1140 ax-16 1210 ax-11o 1218 ax-ext 1459

This theorem depends on definitions: df-bi 147 df-or 224 df-an 225 df-ex 981 df-sb 1172 df-clab 1464 df-cleq 1469 df-clel 1472 df-ne 1587 df-ral 1649 df-rex 1650 df-v 1812 df-dif 2049 df-nul 2281