![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > eqtr3i | Unicode version |
Description: An equality transitivity inference. (Contributed by NM, 6-May-1994.) |
Ref | Expression |
---|---|
eqtr3i.1 |
![]() ![]() ![]() ![]() |
eqtr3i.2 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
eqtr3i |
![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqtr3i.1 |
. . 3
![]() ![]() ![]() ![]() | |
2 | 1 | eqcomi 2181 |
. 2
![]() ![]() ![]() ![]() |
3 | eqtr3i.2 |
. 2
![]() ![]() ![]() ![]() | |
4 | 2, 3 | eqtri 2198 |
1
![]() ![]() ![]() ![]() |
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: 3eqtr3i 2206 3eqtr3ri 2207 unundi 3298 unundir 3299 inindi 3354 inindir 3355 difun1 3397 difabs 3401 notab 3407 dfrab2 3412 dif0 3495 difdifdirss 3509 tpidm13 3694 intmin2 3872 univ 4478 iunxpconst 4688 dmres 4930 opabresid 4962 rnresi 4987 cnvcnv 5083 rnresv 5090 cnvsn0 5099 cnvsn 5113 resdmres 5122 coi2 5147 coires1 5148 dfdm2 5165 isarep2 5305 ssimaex 5579 fnreseql 5628 fmptpr 5710 idref 5759 mpompt 5969 caov31 6066 xpexgALT 6136 cnvoprab 6237 frec0g 6400 unfiin 6927 xpfi 6931 endjusym 7097 halfnqq 7411 caucvgprlemm 7669 caucvgprprlemmu 7696 caucvgsr 7803 mvlladdi 8177 8th4div3 9140 nneoor 9357 nummac 9430 numadd 9432 numaddc 9433 nummul1c 9434 decbin0 9525 infrenegsupex 9596 iseqvalcbv 10459 m1expcl2 10544 facnn 10709 fac0 10710 4bc3eq4 10755 fihasheq0 10775 resqrexlemcalc1 11025 sqrt1 11057 sqrt4 11058 sqrt9 11059 infxrnegsupex 11273 isumss2 11403 geo2sum2 11525 geoihalfsum 11532 sin0 11739 efival 11742 ef01bndlem 11766 cos2bnd 11770 sin4lt0 11776 flodddiv4 11941 2prm 12129 znnen 12401 ennnfonelemhf1o 12416 setsslid 12515 ressressg 12536 metreslem 13919 retopbas 14062 sinhalfpilem 14251 sincos6thpi 14302 sincos3rdpi 14303 lgsdir2lem3 14470 lgseisenlem1 14489 lgseisenlem2 14490 2lgsoddprmlem2 14493 |
Copyright terms: Public domain | W3C validator |