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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 2319 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | nfeq2.1 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfeq 2327 | 1 ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 Ⅎwnf 1460 Ⅎwnfc 2306 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-cleq 2170 df-clel 2173 df-nfc 2308 |
This theorem is referenced by: issetf 2746 eqvincf 2864 csbhypf 3097 nfpr 3644 intab 3875 nfmpt 4097 cbvmptf 4099 cbvmpt 4100 repizf2 4164 moop2 4253 eusvnf 4455 elrnmpt1 4880 fmptco 5685 elabrex 5761 elabrexg 5762 nfmpo 5947 cbvmpox 5956 ovmpodxf 6003 fmpox 6204 f1od2 6239 nfrecs 6311 erovlem 6630 xpf1o 6847 mapxpen 6851 mkvprop 7159 cc3 7270 lble 8907 nfsum1 11367 nfsum 11368 zsumdc 11395 fsum3 11398 fsum3cvg2 11405 fsum2dlemstep 11445 mertenslem2 11547 nfcprod1 11565 nfcprod 11566 zproddc 11590 fprod2dlemstep 11633 ctiunctlemfo 12443 ellimc3apf 14317 |
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