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Mirrors > Home > ILE Home > Th. List > addcl | Unicode version |
Description: Alias for ax-addcl 7909, for naming consistency with addcli 7963. Use this theorem instead of ax-addcl 7909 or axaddcl 7865. (Contributed by NM, 10-Mar-2008.) |
Ref | Expression |
---|---|
addcl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-addcl 7909 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-addcl 7909 |
This theorem is referenced by: adddir 7950 0cn 7951 addcli 7963 addcld 7979 muladd11 8092 peano2cn 8094 muladd11r 8115 add4 8120 cnegexlem3 8136 cnegex 8137 0cnALT 8149 negeu 8150 pncan 8165 2addsub 8173 addsubeq4 8174 nppcan2 8190 ppncan 8201 muladd 8343 mulsub 8360 recexap 8612 muleqadd 8627 conjmulap 8688 halfaddsubcl 9154 halfaddsub 9155 serf 10476 ser3add 10507 ser3sub 10508 ser0 10516 binom2 10634 binom3 10640 bernneq 10643 shftlem 10827 shftval2 10837 shftval5 10840 2shfti 10842 crre 10868 crim 10869 cjadd 10895 addcj 10902 sqabsadd 11066 absreimsq 11078 absreim 11079 abstri 11115 addcn2 11320 climadd 11336 clim2ser 11347 clim2ser2 11348 isermulc2 11350 serf0 11362 sumrbdclem 11387 fsum3cvg 11388 summodclem3 11390 summodclem2a 11391 zsumdc 11394 fsum3 11397 fsum3cvg2 11404 fsum3ser 11407 fsumcl2lem 11408 fsumcl 11410 sumsnf 11419 fsummulc2 11458 binom 11494 isumshft 11500 isumsplit 11501 geolim2 11522 cvgratnnlemseq 11536 cvgratz 11542 ef0lem 11670 efcj 11683 ef4p 11704 efgt1p 11706 tanval3ap 11724 efi4p 11727 sinadd 11746 cosadd 11747 tanaddap 11749 addsin 11752 demoivreALT 11783 opoe 11902 pythagtriplem4 12270 pythagtriplem12 12277 gzaddcl 12377 cncrng 13502 addccncf 14125 dvaddxxbr 14204 dvaddxx 14206 dviaddf 14208 dveflem 14226 sinperlem 14268 ptolemy 14284 tangtx 14298 sinkpi 14307 binom4 14436 2sqlem2 14501 |
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