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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 2655 rabbiia 2722 cbvrab 2735 cbvcsbw 3061 cbvcsb 3062 csbco 3067 csbcow 3068 cbvrabcsf 3122 un4 3295 in13 3348 in31 3349 in4 3351 indifcom 3381 indir 3384 undir 3385 notrab 3412 dfnul3 3425 rab0 3451 prcom 3668 tprot 3685 tpcoma 3686 tpcomb 3687 tpass 3688 qdassr 3690 pw0 3739 opid 3796 int0 3858 cbviun 3923 cbviin 3924 iunrab 3934 iunin1 3951 cbvopab 4074 cbvopab1 4076 cbvopab2 4077 cbvopab1s 4078 cbvopab2v 4080 unopab 4082 cbvmptf 4097 cbvmpt 4098 iunopab 4281 uniuni 4451 2ordpr 4523 rabxp 4663 fconstmpt 4673 inxp 4761 cnvco 4812 rnmpt 4875 resundi 4920 resundir 4921 resindi 4922 resindir 4923 rescom 4932 resima 4940 imadmrn 4980 cnvimarndm 4992 cnvi 5033 rnun 5037 imaundi 5041 cnvxp 5047 imainrect 5074 imacnvcnv 5093 resdmres 5120 imadmres 5121 mptpreima 5122 cbviota 5183 sb8iota 5185 resdif 5483 cbvriota 5840 dfoprab2 5921 cbvoprab1 5946 cbvoprab2 5947 cbvoprab12 5948 cbvoprab3 5950 cbvmpox 5952 resoprab 5970 caov32 6061 caov31 6063 ofmres 6136 dfopab2 6189 dfxp3 6194 dmmpossx 6199 fmpox 6200 tposco 6275 mapsncnv 6694 cbvixp 6714 xpcomco 6825 sbthlemi6 6960 xp2dju 7213 djuassen 7215 dmaddpi 7323 dmmulpi 7324 dfplpq2 7352 dfmpq2 7353 dmaddpq 7377 dmmulpq 7378 axi2m1 7873 negiso 8911 nummac 9427 decsubi 9445 9t11e99 9512 fzprval 10081 fztpval 10082 sqdivapi 10603 binom2i 10628 4bc2eq6 10753 shftidt2 10840 cji 10910 xrnegiso 11269 cbvsum 11367 fsumrelem 11478 cbvprod 11565 nn0gcdsq 12199 cnfldsub 13439 dvdsrzring 13463 restco 13644 cnmptid 13751 sincos3rdpi 14234 lgsdir2lem5 14403 2lgsoddprmlem3d 14428 if0ab 14527 |
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