![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > eqeltrri | Unicode version |
Description: Substitution of equal classes into membership relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eqeltrr.1 |
![]() ![]() ![]() ![]() |
eqeltrr.2 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
eqeltrri |
![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeltrr.1 |
. . 3
![]() ![]() ![]() ![]() | |
2 | 1 | eqcomi 2181 |
. 2
![]() ![]() ![]() ![]() |
3 | eqeltrr.2 |
. 2
![]() ![]() ![]() ![]() | |
4 | 2, 3 | eqeltri 2250 |
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-ie1 1493 ax-ie2 1494 ax-4 1510 ax-17 1526 ax-ial 1534 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 df-clel 2173 |
This theorem is referenced by: 3eltr3i 2258 p0ex 4185 epse 4339 unex 4438 ordtri2orexmid 4519 onsucsssucexmid 4523 ordsoexmid 4558 ordtri2or2exmid 4567 ontri2orexmidim 4568 nnregexmid 4617 abrexex 6112 opabex3 6117 abrexex2 6119 abexssex 6120 abexex 6121 oprabrexex2 6125 tfr0dm 6317 exmidonfinlem 7186 1lt2pi 7327 prarloclemarch2 7406 prarloclemlt 7480 0cn 7937 resubcli 8207 0reALT 8241 10nn 9385 numsucc 9409 nummac 9414 qreccl 9628 unirnioo 9957 fz0to4untppr 10107 fn0g 12683 sn0topon 13248 retopbas 13683 blssioo 13705 lgslem4 14064 bj-unex 14320 exmidsbthrlem 14419 |
Copyright terms: Public domain | W3C validator |