num0u - Intuitionistic Logic Explorer

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Theorem num0u 9332

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 9152	. . . 4
4	3	nn0cni 9126	. . 3
5	4	addid1i 8040	. 2
6	5	eqcomi 2169	1

Colors of variables: wff set class

Syntax hints:

wceq 1343

wcel 2136 (class class class)co 5842

cc0 7753

caddc 7756

cmul 7758

cn0 9114

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-14 2139 ax-ext 2147 ax-sep 4100 ax-pow 4153 ax-pr 4187 ax-setind 4514 ax-cnex 7844 ax-resscn 7845 ax-1cn 7846 ax-1re 7847 ax-icn 7848 ax-addcl 7849 ax-addrcl 7850 ax-mulcl 7851 ax-addcom 7853 ax-mulcom 7854 ax-addass 7855 ax-mulass 7856 ax-distr 7857 ax-i2m1 7858 ax-1rid 7860 ax-0id 7861 ax-rnegex 7862 ax-cnre 7864

This theorem depends on definitions: df-bi 116 df-3an 970 df-tru 1346 df-fal 1349 df-nf 1449 df-sb 1751 df-eu 2017 df-mo 2018 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-ne 2337 df-ral 2449 df-rex 2450 df-reu 2451 df-rab 2453 df-v 2728 df-sbc 2952 df-dif 3118 df-un 3120 df-in 3122 df-ss 3129 df-pw 3561 df-sn 3582 df-pr 3583 df-op 3585 df-uni 3790 df-int 3825 df-br 3983 df-opab 4044 df-id 4271 df-xp 4610 df-rel 4611 df-cnv 4612 df-co 4613 df-dm 4614 df-iota 5153 df-fun 5190 df-fv 5196 df-riota 5798 df-ov 5845 df-oprab 5846 df-mpo 5847 df-sub 8071 df-inn 8858 df-n0 9115

This theorem is referenced by: dec0u 9342 numsucc 9361 nummul1c 9370