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Mirrors > Home > ILE Home > Th. List > csbeq1 | Unicode version |
Description: Analog of dfsbcq 2884 for proper substitution into a class. (Contributed by NM, 10-Nov-2005.) |
Ref | Expression |
---|---|
csbeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq 2884 | . . 3 | |
2 | 1 | abbidv 2235 | . 2 |
3 | df-csb 2976 | . 2 | |
4 | df-csb 2976 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2175 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1316 wcel 1465 cab 2103 wsbc 2882 csb 2975 |
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 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-sbc 2883 df-csb 2976 |
This theorem is referenced by: csbeq1d 2981 csbeq1a 2983 csbiebg 3012 sbcnestgf 3021 cbvralcsf 3032 cbvrexcsf 3033 cbvreucsf 3034 cbvrabcsf 3035 csbing 3253 disjnims 3891 sbcbrg 3952 csbopabg 3976 pofun 4204 csbima12g 4870 csbiotag 5086 fvmpts 5467 fvmpt2 5472 mptfvex 5474 elfvmptrab1 5483 fmptcof 5555 fmptcos 5556 fliftfuns 5667 csbriotag 5710 csbov123g 5777 eqerlem 6428 qliftfuns 6481 summodclem2a 11118 zsumdc 11121 fsum3 11124 sumsnf 11146 sumsns 11152 fsum2dlemstep 11171 fisumcom2 11175 fsumshftm 11182 fisum0diag2 11184 fsumiun 11214 ctiunctlemf 11878 mulcncflem 12686 |
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