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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 |
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nfeq.2 |
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Ref | Expression |
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nfeq |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfcleq 2183 |
. 2
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2 | nfnfc.1 |
. . . . 5
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3 | 2 | nfcri 2326 |
. . . 4
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4 | nfeq.2 |
. . . . 5
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5 | 4 | nfcri 2326 |
. . . 4
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6 | 3, 5 | nfbi 1600 |
. . 3
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7 | 6 | nfal 1587 |
. 2
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8 | 1, 7 | nfxfr 1485 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-cleq 2182 df-clel 2185 df-nfc 2321 |
This theorem is referenced by: nfel 2341 nfeq1 2342 nfeq2 2344 nfne 2453 raleqf 2682 rexeqf 2683 reueq1f 2684 rmoeq1f 2685 rabeqf 2742 sbceqg 3088 csbhypf 3110 nfiotadw 5196 nffn 5327 nffo 5452 fvmptdf 5619 mpteqb 5622 fvmptf 5624 eqfnfv2f 5633 dff13f 5787 ovmpos 6015 ov2gf 6016 ovmpodxf 6017 ovmpodf 6023 eqerlem 6584 sumeq2 11385 fsumadd 11432 prodeq1f 11578 prodeq2 11583 txcnp 14155 cnmpt11 14167 cnmpt21 14175 cnmptcom 14182 lgseisenlem2 14835 |
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