axunprim - Mathbox for Scott Fenton

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Theorem axunprim 31580

Description: ax-un 6949 without distinct variable conditions or defined symbols. (Contributed by Scott Fenton, 13-Oct-2010.)

**Assertion**
Ref	Expression
axunprim

**Proof of Theorem axunprim**
Step	Hyp	Ref	Expression
1		axunnd 9418	. 2 $/\$
2		df-an 386	. . . . . . . 8 $/\$
3	2	exbii 1774	. . . . . . 7 $/\$
4		exnal 1754	. . . . . . 7
5	3, 4	bitri 264	. . . . . 6 $/\$
6	5	imbi1i 339	. . . . 5 $/\$
7	6	albii 1747	. . . 4 $/\$
8	7	exbii 1774	. . 3 $/\$
9		df-ex 1705	. . 3
10	8, 9	bitri 264	. 2 $/\$
11	1, 10	mpbi 220	1

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4 $/\$ wa 384

wal 1481

wex 1704

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 ax-un 6949 ax-reg 8497

This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-eprel 5029 df-fr 5073

This theorem is referenced by: (None)