subsub3 - Intuitionistic Logic Explorer

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Theorem subsub3 8126

Description: Law for double subtraction. (Contributed by NM, 27-Jul-2005.)

**Assertion**
Ref	Expression
subsub3	$/\$ $/\$

**Proof of Theorem subsub3**
Step	Hyp	Ref	Expression
1		subsub2 8122	. 2 $/\$ $/\$
2		addsubass 8104	. . 3 $/\$ $/\$
3	2	3com23 1199	. 2 $/\$ $/\$
4	1, 3	eqtr4d 2201	1 $/\$ $/\$

Colors of variables: wff set class

Syntax hints:

wi 4 $/\$ w3a 968

wceq 1343

wcel 2136 (class class class)co 5841

cc 7747

caddc 7752

cmin 8065

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 4099 ax-pow 4152 ax-pr 4186 ax-setind 4513 ax-resscn 7841 ax-1cn 7842 ax-icn 7844 ax-addcl 7845 ax-addrcl 7846 ax-mulcl 7847 ax-addcom 7849 ax-addass 7851 ax-distr 7853 ax-i2m1 7854 ax-0id 7857 ax-rnegex 7858 ax-cnre 7860

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 2296 df-ne 2336 df-ral 2448 df-rex 2449 df-reu 2450 df-rab 2452 df-v 2727 df-sbc 2951 df-dif 3117 df-un 3119 df-in 3121 df-ss 3128 df-pw 3560 df-sn 3581 df-pr 3582 df-op 3584 df-uni 3789 df-br 3982 df-opab 4043 df-id 4270 df-xp 4609 df-rel 4610 df-cnv 4611 df-co 4612 df-dm 4613 df-iota 5152 df-fun 5189 df-fv 5195 df-riota 5797 df-ov 5844 df-oprab 5845 df-mpo 5846 df-sub 8067

This theorem is referenced by: subsub3d 8235 nnsub 8892 cos2t 11687 ndvdsadd 11864