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Mirrors > Home > ILE Home > Th. List > csbeq1 | Unicode version |
Description: Analog of dfsbcq 2957 for proper substitution into a class. (Contributed by NM, 10-Nov-2005.) |
Ref | Expression |
---|---|
csbeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq 2957 | . . 3 | |
2 | 1 | abbidv 2288 | . 2 |
3 | df-csb 3050 | . 2 | |
4 | df-csb 3050 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2228 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 cab 2156 wsbc 2955 csb 3049 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-sbc 2956 df-csb 3050 |
This theorem is referenced by: csbeq1d 3056 csbeq1a 3058 csbiebg 3091 sbcnestgf 3100 cbvralcsf 3111 cbvrexcsf 3112 cbvreucsf 3113 cbvrabcsf 3114 csbing 3334 disjnims 3981 sbcbrg 4043 csbopabg 4067 pofun 4297 csbima12g 4972 csbiotag 5191 fvmpts 5574 fvmpt2 5579 mptfvex 5581 elfvmptrab1 5590 fmptcof 5663 fmptcos 5664 fliftfuns 5777 csbriotag 5821 csbov123g 5891 eqerlem 6544 qliftfuns 6597 summodclem2a 11344 zsumdc 11347 fsum3 11350 sumsnf 11372 sumsns 11378 fsum2dlemstep 11397 fisumcom2 11401 fsumshftm 11408 fisum0diag2 11410 fsumiun 11440 prodsnf 11555 fprodm1s 11564 fprodp1s 11565 prodsns 11566 fprod2dlemstep 11585 fprodcom2fi 11589 pcmptdvds 12297 ctiunctlemf 12393 mulcncflem 13384 |
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