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Mirrors > Home > ILE Home > Th. List > nfeq | Unicode version |
Description: Hypothesis builder for equality. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfnfc.1 | |
nfeq.2 |
Ref | Expression |
---|---|
nfeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfcleq 2111 | . 2 | |
2 | nfnfc.1 | . . . . 5 | |
3 | 2 | nfcri 2252 | . . . 4 |
4 | nfeq.2 | . . . . 5 | |
5 | 4 | nfcri 2252 | . . . 4 |
6 | 3, 5 | nfbi 1553 | . . 3 |
7 | 6 | nfal 1540 | . 2 |
8 | 1, 7 | nfxfr 1435 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1314 wceq 1316 wnf 1421 wcel 1465 wnfc 2245 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-cleq 2110 df-clel 2113 df-nfc 2247 |
This theorem is referenced by: nfel 2267 nfeq1 2268 nfeq2 2270 nfne 2378 raleqf 2599 rexeqf 2600 reueq1f 2601 rmoeq1f 2602 rabeqf 2650 sbceqg 2989 csbhypf 3008 nfiotadxy 5061 nffn 5189 nffo 5314 fvmptdf 5476 mpteqb 5479 fvmptf 5481 eqfnfv2f 5490 dff13f 5639 ovmpos 5862 ov2gf 5863 ovmpodxf 5864 ovmpodf 5870 eqerlem 6428 sumeq2 11096 fsumadd 11143 txcnp 12367 cnmpt11 12379 cnmpt21 12387 cnmptcom 12394 |
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