num0u - Intuitionistic Logic Explorer

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Theorem num0u 9408

Description: Add a zero in the units place. (Contributed by Mario Carneiro, 18-Feb-2014.)

**Hypotheses**
Ref	Expression
numnncl.1
numnncl.2

**Assertion**
Ref	Expression
num0u

**Proof of Theorem num0u**
Step	Hyp	Ref	Expression
1		numnncl.1	. . . . 5
2		numnncl.2	. . . . 5
3	1, 2	nn0mulcli 9228	. . . 4
4	3	nn0cni 9202	. . 3
5	4	addid1i 8113	. 2
6	5	eqcomi 2191	1

Colors of variables: wff set class

Syntax hints:

wceq 1363

wcel 2158 (class class class)co 5888

cc0 7825

caddc 7828

cmul 7830

cn0 9190

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 ax-setind 4548 ax-cnex 7916 ax-resscn 7917 ax-1cn 7918 ax-1re 7919 ax-icn 7920 ax-addcl 7921 ax-addrcl 7922 ax-mulcl 7923 ax-addcom 7925 ax-mulcom 7926 ax-addass 7927 ax-mulass 7928 ax-distr 7929 ax-i2m1 7930 ax-1rid 7932 ax-0id 7933 ax-rnegex 7934 ax-cnre 7936

This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ne 2358 df-ral 2470 df-rex 2471 df-reu 2472 df-rab 2474 df-v 2751 df-sbc 2975 df-dif 3143 df-un 3145 df-in 3147 df-ss 3154 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-int 3857 df-br 4016 df-opab 4077 df-id 4305 df-xp 4644 df-rel 4645 df-cnv 4646 df-co 4647 df-dm 4648 df-iota 5190 df-fun 5230 df-fv 5236 df-riota 5844 df-ov 5891 df-oprab 5892 df-mpo 5893 df-sub 8144 df-inn 8934 df-n0 9191

This theorem is referenced by: dec0u 9418 numsucc 9437 nummul1c 9446