mulneg12 - Intuitionistic Logic Explorer

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Theorem mulneg12 8276

Description: Swap the negative sign in a product. (Contributed by NM, 30-Jul-2004.)

**Assertion**
Ref	Expression
mulneg12	$/\$

**Proof of Theorem mulneg12**
Step	Hyp	Ref	Expression
1		mulneg1 8274	. 2 $/\$
2		mulneg2 8275	. 2 $/\$
3	1, 2	eqtr4d 2193	1 $/\$

Colors of variables: wff set class

Syntax hints:

wi 4 $/\$ wa 103

wceq 1335

wcel 2128 (class class class)co 5826

cc 7732

cmul 7739

cneg 8051

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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 ax-setind 4498 ax-resscn 7826 ax-1cn 7827 ax-icn 7829 ax-addcl 7830 ax-addrcl 7831 ax-mulcl 7832 ax-addcom 7834 ax-mulcom 7835 ax-addass 7836 ax-distr 7838 ax-i2m1 7839 ax-0id 7842 ax-rnegex 7843 ax-cnre 7845

This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-ral 2440 df-rex 2441 df-reu 2442 df-rab 2444 df-v 2714 df-sbc 2938 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4028 df-id 4255 df-xp 4594 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-iota 5137 df-fun 5174 df-fv 5180 df-riota 5782 df-ov 5829 df-oprab 5830 df-mpo 5831 df-sub 8052 df-neg 8053

This theorem is referenced by: mul2neg 8277 crim 10769 efi4p 11625 sinneg 11634 cosneg 11635 efmival 11641 negdvdsb 11714 divalglemex 11825 bezoutlemaz 11902 bezoutlembz 11903 dvrecap 13147