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Mirrors > Home > ILE Home > Th. List > csbeq1d | Unicode version |
Description: Equality deduction for proper substitution into a class. (Contributed by NM, 3-Dec-2005.) |
Ref | Expression |
---|---|
csbeq1d.1 |
Ref | Expression |
---|---|
csbeq1d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq1d.1 | . 2 | |
2 | csbeq1 3034 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1335 csb 3031 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-sbc 2938 df-csb 3032 |
This theorem is referenced by: csbidmg 3087 csbco3g 3089 fmptcof 5635 mpomptsx 6146 dmmpossx 6148 fmpox 6149 fmpoco 6164 xpf1o 6790 summodclem3 11281 summodclem2a 11282 summodc 11284 zsumdc 11285 fsum3 11288 sumsnf 11310 fsumcnv 11338 fisumcom2 11339 fsumshftm 11346 fisum0diag2 11348 prodmodclem3 11476 prodmodclem2a 11477 prodmodc 11479 zproddc 11480 fprodseq 11484 prodsnf 11493 fprodcnv 11526 fprodcom2fi 11527 ctiunctlemu1st 12205 ctiunctlemu2nd 12206 ctiunctlemudc 12208 ctiunctlemfo 12210 |
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