mulneg12 - Intuitionistic Logic Explorer

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Theorem mulneg12 8690

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 8688	. 2 $/\$
2		mulneg2 8689	. 2 $/\$
3	1, 2	eqtr4d 2270	1 $/\$

Colors of variables: wff set class

Syntax hints:

wi 4 $/\$ wa 104

wceq 1398

wcel 2205 (class class class)co 6060

cc 8143

cmul 8150

cneg 8464

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 619 ax-in2 620 ax-io 717 ax-5 1496 ax-7 1497 ax-gen 1498 ax-ie1 1542 ax-ie2 1543 ax-8 1553 ax-10 1554 ax-11 1555 ax-i12 1556 ax-bndl 1558 ax-4 1559 ax-17 1575 ax-i9 1579 ax-ial 1583 ax-i5r 1584 ax-14 2208 ax-ext 2216 ax-sep 4234 ax-pow 4293 ax-pr 4328 ax-setind 4666 ax-resscn 8237 ax-1cn 8238 ax-icn 8240 ax-addcl 8241 ax-addrcl 8242 ax-mulcl 8243 ax-addcom 8245 ax-mulcom 8246 ax-addass 8247 ax-distr 8249 ax-i2m1 8250 ax-0id 8253 ax-rnegex 8254 ax-cnre 8256

This theorem depends on definitions: df-bi 117 df-3an 1007 df-tru 1401 df-fal 1404 df-nf 1510 df-sb 1812 df-eu 2085 df-mo 2086 df-clab 2221 df-cleq 2227 df-clel 2230 df-nfc 2375 df-ne 2415 df-ral 2527 df-rex 2528 df-reu 2529 df-rab 2531 df-v 2817 df-sbc 3046 df-dif 3216 df-un 3218 df-in 3220 df-ss 3227 df-pw 3677 df-sn 3701 df-pr 3702 df-op 3704 df-uni 3921 df-br 4116 df-opab 4178 df-id 4420 df-xp 4762 df-rel 4763 df-cnv 4764 df-co 4765 df-dm 4766 df-iota 5319 df-fun 5361 df-fv 5367 df-riota 6013 df-ov 6063 df-oprab 6064 df-mpo 6065 df-sub 8465 df-neg 8466

This theorem is referenced by: mul2neg 8691 crim 11573 efi4p 12434 sinneg 12443 cosneg 12444 efmival 12450 negdvdsb 12524 divalglemex 12639 bezoutlemaz 12730 bezoutlembz 12731 dvrecap 15710