Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > syl6eqel | Unicode version |
Description: A membership and equality inference. (Contributed by NM, 4-Jan-2006.) |
Ref | Expression |
---|---|
syl6eqel.1 | |
syl6eqel.2 |
Ref | Expression |
---|---|
syl6eqel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl6eqel.1 | . 2 | |
2 | syl6eqel.2 | . . 3 | |
3 | 2 | a1i 9 | . 2 |
4 | 1, 3 | eqeltrd 2194 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wcel 1465 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-17 1491 ax-ial 1499 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-cleq 2110 df-clel 2113 |
This theorem is referenced by: syl6eqelr 2209 snexprc 4080 onsucelsucexmidlem 4414 dcextest 4465 nnpredcl 4506 ovprc 5774 nnmcl 6345 xpsnen 6683 xpfi 6786 snexxph 6806 ctssdclemn0 6963 exmidonfinlem 7017 indpi 7118 nq0m0r 7232 genpelxp 7287 un0mulcl 8969 znegcl 9043 zeo 9114 eqreznegel 9362 xnegcl 9570 modqid0 10078 q2txmodxeq0 10112 ser0 10242 expcllem 10259 m1expcl2 10270 bcval 10450 bccl 10468 hashinfom 10479 resqrexlemlo 10740 iserge0 11067 sumrbdclem 11100 fsum3cvg 11101 summodclem3 11104 summodclem2a 11105 fisumss 11116 binom 11208 bcxmas 11213 gcdval 11560 gcdcl 11567 lcmcl 11665 ssblps 12505 ssbl 12506 xmeter 12516 blssioo 12625 nninfsellemeqinf 13108 nninffeq 13112 isomninnlem 13121 trilpolemclim 13125 |
Copyright terms: Public domain | W3C validator |