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Mirrors > Home > ILE Home > Th. List > nfeq1 | 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 2332 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfeq 2340 | 1 ⊢ Ⅎ𝑥 𝐴 = 𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1364 Ⅎwnf 1471 Ⅎwnfc 2319 |
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: euabsn 3677 fvmptt 5627 eusvobj2 5881 ovmpodv2 6029 ovi3 6032 dom2lem 6797 seq3f1olemstep 10531 seq3f1olemp 10532 fsumf1o 11429 isumss 11430 isummulc2 11465 fsum00 11501 isumshft 11529 fprodf1o 11627 prodssdc 11628 |
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