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Mirrors > Home > ILE Home > Th. List > pm5.32da | Unicode version |
Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 9-Dec-2006.) |
Ref | Expression |
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pm5.32da.1 |
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Ref | Expression |
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pm5.32da |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm5.32da.1 |
. . 3
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2 | 1 | ex 115 |
. 2
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3 | 2 | pm5.32d 450 |
1
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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 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: rexbida 2485 reubida 2672 rmobida 2677 mpteq12f 4098 reuhypd 4486 funbrfv2b 5576 dffn5im 5577 eqfnfv2 5630 fndmin 5639 fniniseg 5652 rexsupp 5656 fmptco 5698 dff13 5785 riotabidva 5863 mpoeq123dva 5952 mpoeq3dva 5955 mpoxopovel 6260 qliftfun 6635 erovlem 6645 xpcomco 6844 elfi2 6989 ctssdccl 7128 ltexpi 7354 dfplpq2 7371 axprecex 7897 zrevaddcl 9321 qrevaddcl 9662 icoshft 10008 fznn 10107 shftdm 10849 2shfti 10858 sumeq2 11385 fsum3 11413 fsum2dlemstep 11460 prodeq2 11583 fprodseq 11609 gcdaddm 12003 grpidpropdg 12816 ismgmid 12819 mhmpropd 12884 issubm2 12891 eqgid 13131 eqgabl 13228 rngpropd 13270 iscrng2 13330 ringpropd 13353 crngpropd 13354 crngunit 13422 dvdsrpropdg 13458 issubrg3 13555 lsslss 13658 lsspropdg 13708 bastop2 13981 restopn2 14080 iscnp3 14100 lmbr2 14111 txlm 14176 ismet2 14251 xblpnfps 14295 xblpnf 14296 blininf 14321 blres 14331 elmopn2 14346 neibl 14388 metrest 14403 metcnp3 14408 metcnp 14409 metcnp2 14410 metcn 14411 txmetcn 14416 cnbl0 14431 cnblcld 14432 bl2ioo 14439 elcncf2 14458 cncfmet 14476 cnlimc 14538 |
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