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Mirrors > Home > ILE Home > Th. List > 3eqtr4i | Unicode version |
Description: An inference from three chained equalities. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
3eqtr4i.1 |
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3eqtr4i.2 |
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3eqtr4i.3 |
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Ref | Expression |
---|---|
3eqtr4i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eqtr4i.2 |
. 2
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2 | 3eqtr4i.3 |
. . 3
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3 | 3eqtr4i.1 |
. . 3
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4 | 2, 3 | eqtr4i 2201 |
. 2
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5 | 1, 4 | eqtr4i 2201 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() |
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-5 1447 ax-gen 1449 ax-4 1510 ax-17 1526 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 |
This theorem is referenced by: rabswap 2656 rabbiia 2724 cbvrab 2737 cbvcsbw 3063 cbvcsb 3064 csbco 3069 csbcow 3070 cbvrabcsf 3124 un4 3297 in13 3350 in31 3351 in4 3353 indifcom 3383 indir 3386 undir 3387 notrab 3414 dfnul3 3427 rab0 3453 prcom 3670 tprot 3687 tpcoma 3688 tpcomb 3689 tpass 3690 qdassr 3692 pw0 3741 opid 3798 int0 3860 cbviun 3925 cbviin 3926 iunrab 3936 iunin1 3953 cbvopab 4076 cbvopab1 4078 cbvopab2 4079 cbvopab1s 4080 cbvopab2v 4082 unopab 4084 cbvmptf 4099 cbvmpt 4100 iunopab 4283 uniuni 4453 2ordpr 4525 rabxp 4665 fconstmpt 4675 inxp 4763 cnvco 4814 rnmpt 4877 resundi 4922 resundir 4923 resindi 4924 resindir 4925 rescom 4934 resima 4942 imadmrn 4982 cnvimarndm 4994 cnvi 5035 rnun 5039 imaundi 5043 cnvxp 5049 imainrect 5076 imacnvcnv 5095 resdmres 5122 imadmres 5123 mptpreima 5124 cbviota 5185 sb8iota 5187 resdif 5485 cbvriota 5843 dfoprab2 5924 cbvoprab1 5949 cbvoprab2 5950 cbvoprab12 5951 cbvoprab3 5953 cbvmpox 5955 resoprab 5973 caov32 6064 caov31 6066 ofmres 6139 dfopab2 6192 dfxp3 6197 dmmpossx 6202 fmpox 6203 tposco 6278 mapsncnv 6697 cbvixp 6717 xpcomco 6828 sbthlemi6 6963 xp2dju 7216 djuassen 7218 dmaddpi 7326 dmmulpi 7327 dfplpq2 7355 dfmpq2 7356 dmaddpq 7380 dmmulpq 7381 axi2m1 7876 negiso 8914 nummac 9430 decsubi 9448 9t11e99 9515 fzprval 10084 fztpval 10085 sqdivapi 10606 binom2i 10631 4bc2eq6 10756 shftidt2 10843 cji 10913 xrnegiso 11272 cbvsum 11370 fsumrelem 11481 cbvprod 11568 nn0gcdsq 12202 rmodislmod 13446 cnfldsub 13508 dvdsrzring 13532 restco 13713 cnmptid 13820 sincos3rdpi 14303 lgsdir2lem5 14472 2lgsoddprmlem3d 14497 if0ab 14596 |
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