![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > csbeq1a | Unicode version |
Description: Equality theorem for proper substitution into a class. (Contributed by NM, 10-Nov-2005.) |
Ref | Expression |
---|---|
csbeq1a |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbid 3015 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | csbeq1 3010 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | syl5eqr 2187 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-sbc 2914 df-csb 3008 |
This theorem is referenced by: csbhypf 3043 csbiebt 3044 sbcnestgf 3056 cbvralcsf 3067 cbvrexcsf 3068 cbvreucsf 3069 cbvrabcsf 3070 csbing 3288 disjnims 3929 disjiun 3932 sbcbrg 3990 moop2 4181 pofun 4242 eusvnf 4382 opeliunxp 4602 elrnmpt1 4798 resmptf 4877 csbima12g 4908 fvmpts 5507 fvmpt2 5512 mptfvex 5514 fmptco 5594 fmptcof 5595 fmptcos 5596 elabrex 5667 fliftfuns 5707 csbov123g 5817 ovmpos 5902 csbopeq1a 6094 mpomptsx 6103 dmmpossx 6105 fmpox 6106 mpofvex 6109 fmpoco 6121 disjxp1 6141 eqerlem 6468 qliftfuns 6521 mptelixpg 6636 xpf1o 6746 iunfidisj 6842 cc3 7100 seq3f1olemstep 10305 seq3f1olemp 10306 sumeq2 11160 sumfct 11175 sumrbdclem 11178 summodclem3 11181 summodclem2a 11182 zsumdc 11185 fsumgcl 11187 fsum3 11188 isumss 11192 isumss2 11194 fsum3cvg2 11195 fsumzcl2 11206 fsumsplitf 11209 sumsnf 11210 sumsns 11216 fsumsplitsnun 11220 fsum2dlemstep 11235 fsumcnv 11238 fisumcom2 11239 fsumshftm 11246 fisum0diag2 11248 fsummulc2 11249 fsum00 11263 fsumabs 11266 fsumrelem 11272 fsumiun 11278 isumshft 11291 mertenslem2 11337 prodeq2 11358 prodrbdclem 11372 prodmodclem3 11376 prodmodclem2a 11377 zproddc 11380 fprodseq 11384 ctiunctlemudc 11986 ctiunctlemf 11987 ctiunctal 11990 iuncld 12323 fsumcncntop 12764 limcmpted 12840 |
Copyright terms: Public domain | W3C validator |