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Mirrors > Home > MPE Home > Th. List > nfeq1 | Structured version Visualization version GIF version |
Description: Hypothesis builder for equality, special case. (Contributed by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
nfeq1.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfeq1 | ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfeq1.1 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | nfcv 2974 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfeq 2988 | 1 ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 Ⅎwnf 1775 Ⅎwnfc 2958 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-9 2115 ax-10 2136 ax-11 2151 ax-12 2167 ax-ext 2790 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-cleq 2811 df-nfc 2960 |
This theorem is referenced by: euabsn 4654 invdisjrabw 5042 invdisjrab 5043 disjxun 5055 iunopeqop 5402 fvelimad 6725 opabiotafun 6737 fvmptt 6780 eusvobj2 7138 oprabv 7203 ovmpodv2 7297 ov3 7300 dom2lem 8537 pwfseqlem2 10069 fsumf1o 15068 isummulc2 15105 fsum00 15141 isumshft 15182 zprod 15279 fprodf1o 15288 prodss 15289 fprodle 15338 iserodd 16160 yonedalem4b 17514 gsum2d2lem 19022 gsummptnn0fz 19035 gsummoncoe1 20400 elptr2 22110 ovoliunnul 24035 mbfinf 24193 itg2splitlem 24276 dgrle 24760 disjabrex 30260 disjabrexf 30261 disjunsn 30272 voliune 31387 volfiniune 31388 bnj958 32111 bnj1491 32226 finminlem 33563 poimirlem23 34796 poimirlem28 34801 cdleme43fsv1snlem 37436 ltrniotaval 37597 cdlemksv2 37863 cdlemkuv2 37883 cdlemk36 37929 cdlemkid 37952 cdlemk19x 37959 eq0rabdioph 39251 monotoddzz 39418 stoweidlem28 42190 stoweidlem48 42210 stoweidlem58 42220 etransclem32 42428 sge0gtfsumgt 42602 voliunsge0lem 42631 |
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