subsub3 - Intuitionistic Logic Explorer

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Theorem subsub3 8374

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 8370	. 2 $/\$ $/\$
2		addsubass 8352	. . 3 $/\$ $/\$
3	2	3com23 1233	. 2 $/\$ $/\$
4	1, 3	eqtr4d 2265	1 $/\$ $/\$

Colors of variables: wff set class

Syntax hints:

wi 4 $/\$ w3a 1002

wceq 1395

wcel 2200 (class class class)co 6000

cc 7993

caddc 7998

cmin 8313

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 617 ax-in2 618 ax-io 714 ax-5 1493 ax-7 1494 ax-gen 1495 ax-ie1 1539 ax-ie2 1540 ax-8 1550 ax-10 1551 ax-11 1552 ax-i12 1553 ax-bndl 1555 ax-4 1556 ax-17 1572 ax-i9 1576 ax-ial 1580 ax-i5r 1581 ax-14 2203 ax-ext 2211 ax-sep 4201 ax-pow 4257 ax-pr 4292 ax-setind 4628 ax-resscn 8087 ax-1cn 8088 ax-icn 8090 ax-addcl 8091 ax-addrcl 8092 ax-mulcl 8093 ax-addcom 8095 ax-addass 8097 ax-distr 8099 ax-i2m1 8100 ax-0id 8103 ax-rnegex 8104 ax-cnre 8106

This theorem depends on definitions: df-bi 117 df-3an 1004 df-tru 1398 df-fal 1401 df-nf 1507 df-sb 1809 df-eu 2080 df-mo 2081 df-clab 2216 df-cleq 2222 df-clel 2225 df-nfc 2361 df-ne 2401 df-ral 2513 df-rex 2514 df-reu 2515 df-rab 2517 df-v 2801 df-sbc 3029 df-dif 3199 df-un 3201 df-in 3203 df-ss 3210 df-pw 3651 df-sn 3672 df-pr 3673 df-op 3675 df-uni 3888 df-br 4083 df-opab 4145 df-id 4383 df-xp 4724 df-rel 4725 df-cnv 4726 df-co 4727 df-dm 4728 df-iota 5277 df-fun 5319 df-fv 5325 df-riota 5953 df-ov 6003 df-oprab 6004 df-mpo 6005 df-sub 8315

This theorem is referenced by: subsub3d 8483 nnsub 9145 cos2t 12256 ndvdsadd 12437