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| Mirrors > Home > ILE Home > Th. List > nfeq2 | GIF version | ||
| Description: Hypothesis builder for equality, special case. (Contributed by Mario Carneiro, 10-Oct-2016.) |
| Ref | Expression |
|---|---|
| nfeq2.1 | ⊢ Ⅎ𝑥𝐵 |
| Ref | Expression |
|---|---|
| nfeq2 | ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfcv 2347 | . 2 ⊢ Ⅎ𝑥𝐴 | |
| 2 | nfeq2.1 | . 2 ⊢ Ⅎ𝑥𝐵 | |
| 3 | 1, 2 | nfeq 2355 | 1 ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
| Colors of variables: wff set class |
| Syntax hints: = wceq 1372 Ⅎwnf 1482 Ⅎwnfc 2334 |
| 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 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-ext 2186 |
| This theorem depends on definitions: df-bi 117 df-tru 1375 df-nf 1483 df-sb 1785 df-cleq 2197 df-clel 2200 df-nfc 2336 |
| This theorem is referenced by: issetf 2778 eqvincf 2897 csbhypf 3131 nfpr 3682 intab 3913 nfmpt 4135 cbvmptf 4137 cbvmpt 4138 repizf2 4205 moop2 4294 eusvnf 4498 elrnmpt1 4927 iotaexab 5247 fmptco 5740 elabrex 5816 elabrexg 5817 nfmpo 6004 cbvmpox 6013 ovmpodxf 6061 fmpox 6276 f1od2 6311 nfrecs 6383 erovlem 6704 xpf1o 6923 mapxpen 6927 mkvprop 7242 cc3 7362 lble 9002 nfsum1 11586 nfsum 11587 zsumdc 11614 fsum3 11617 fsum3cvg2 11624 fsum2dlemstep 11664 mertenslem2 11766 nfcprod1 11784 nfcprod 11785 zproddc 11809 fprod2dlemstep 11852 ctiunctlemfo 12729 ellimc3apf 15050 |
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