num0u - Intuitionistic Logic Explorer

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Theorem num0u 8986

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 8809	. . . 4
4	3	nn0cni 8783	. . 3
5	4	addid1i 7721	. 2
6	5	eqcomi 2099	1

Colors of variables: wff set class

Syntax hints:

wceq 1296

wcel 1445 (class class class)co 5690

cc0 7447

caddc 7450

cmul 7452

cn0 8771

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 582 ax-in2 583 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-14 1457 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 ax-pow 4030 ax-pr 4060 ax-setind 4381 ax-cnex 7533 ax-resscn 7534 ax-1cn 7535 ax-1re 7536 ax-icn 7537 ax-addcl 7538 ax-addrcl 7539 ax-mulcl 7540 ax-addcom 7542 ax-mulcom 7543 ax-addass 7544 ax-mulass 7545 ax-distr 7546 ax-i2m1 7547 ax-1rid 7549 ax-0id 7550 ax-rnegex 7551 ax-cnre 7553

This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-fal 1302 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ne 2263 df-ral 2375 df-rex 2376 df-reu 2377 df-rab 2379 df-v 2635 df-sbc 2855 df-dif 3015 df-un 3017 df-in 3019 df-ss 3026 df-pw 3451 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-int 3711 df-br 3868 df-opab 3922 df-id 4144 df-xp 4473 df-rel 4474 df-cnv 4475 df-co 4476 df-dm 4477 df-iota 5014 df-fun 5051 df-fv 5057 df-riota 5646 df-ov 5693 df-oprab 5694 df-mpt2 5695 df-sub 7752 df-inn 8521 df-n0 8772

This theorem is referenced by: dec0u 8996 numsucc 9015 nummul1c 9024