num0h - Intuitionistic Logic Explorer

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Theorem num0h 9468

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

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

**Assertion**
Ref	Expression
num0h

**Proof of Theorem num0h**
Step	Hyp	Ref	Expression
1		numnncl.1	. . . . 5
2	1	nn0cni 9261	. . . 4
3	2	mul01i 8417	. . 3
4	3	oveq1i 5932	. 2
5		numnncl.2	. . . 4
6	5	nn0cni 9261	. . 3
7	6	addlidi 8169	. 2
8	4, 7	eqtr2i 2218	1

Colors of variables: wff set class

Syntax hints:

wceq 1364

wcel 2167 (class class class)co 5922

cc0 7879

caddc 7882

cmul 7884

cn0 9249

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 1461 ax-7 1462 ax-gen 1463 ax-ie1 1507 ax-ie2 1508 ax-8 1518 ax-10 1519 ax-11 1520 ax-i12 1521 ax-bndl 1523 ax-4 1524 ax-17 1540 ax-i9 1544 ax-ial 1548 ax-i5r 1549 ax-14 2170 ax-ext 2178 ax-sep 4151 ax-pow 4207 ax-pr 4242 ax-setind 4573 ax-cnex 7970 ax-resscn 7971 ax-1cn 7972 ax-1re 7973 ax-icn 7974 ax-addcl 7975 ax-addrcl 7976 ax-mulcl 7977 ax-addcom 7979 ax-mulcom 7980 ax-addass 7981 ax-distr 7983 ax-i2m1 7984 ax-0id 7987 ax-rnegex 7988 ax-cnre 7990

This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1475 df-sb 1777 df-eu 2048 df-mo 2049 df-clab 2183 df-cleq 2189 df-clel 2192 df-nfc 2328 df-ne 2368 df-ral 2480 df-rex 2481 df-reu 2482 df-rab 2484 df-v 2765 df-sbc 2990 df-dif 3159 df-un 3161 df-in 3163 df-ss 3170 df-pw 3607 df-sn 3628 df-pr 3629 df-op 3631 df-uni 3840 df-int 3875 df-br 4034 df-opab 4095 df-id 4328 df-xp 4669 df-rel 4670 df-cnv 4671 df-co 4672 df-dm 4673 df-iota 5219 df-fun 5260 df-fv 5266 df-riota 5877 df-ov 5925 df-oprab 5926 df-mpo 5927 df-sub 8199 df-inn 8991 df-n0 9250

This theorem is referenced by: dec0h 9478 numlti 9493 nummul1c 9505