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Mirrors > Home > MPE Home > Th. List > imim1i | Unicode version |
Description: Inference adding common consequents in an implication, thereby interchanging the original antecedent and consequent. (Contributed by NM, 28-Dec-1992.) (Proof shortened by Wolf Lammen, 4-Aug-2012.) |
Ref | Expression |
---|---|
imim1i.1 |
Ref | Expression |
---|---|
imim1i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imim1i.1 | . 2 | |
2 | id 22 | . 2 | |
3 | 1, 2 | imim12i 57 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -> wi 4 |
This theorem is referenced by: jarr 98 impt 157 jarl 163 bi3antOLD 289 pm2.67-2 402 pm3.41 559 pm3.42 560 jaob 783 3jaob 1290 merco1 1546 19.21v 1729 19.39 1757 r19.37 3006 axrep2 4565 dmcosseq 5269 fliftfun 6210 tz7.48lem 7125 ac6sfi 7784 frfi 7785 domunfican 7813 iunfi 7828 finsschain 7847 cantnfval2 8109 cantnflt 8112 cantnfval2OLD 8139 cantnfltOLD 8142 cnfcom 8165 cnfcomOLD 8173 kmlem1 8551 kmlem13 8563 axpowndlem2 8994 axpowndlem2OLD 8995 wunfi 9120 ingru 9214 xrub 11532 hashf1lem2 12505 caubnd 13191 fsum2d 13586 fsumabs 13615 fsumrlim 13625 fsumo1 13626 fsumiun 13635 fprod2d 13785 ablfac1eulem 17123 mplcoe1 18127 mplcoe5 18131 mplcoe2OLD 18133 mdetunilem9 19122 t1t0 19849 fiuncmp 19904 ptcmpfi 20314 isfil2 20357 fsumcn 21374 ovolfiniun 21912 finiunmbl 21954 volfiniun 21957 itgfsum 22233 dvmptfsum 22376 pntrsumbnd 23751 nbgraf1olem1 24441 nmounbseqi 25692 nmounbseqiOLD 25693 isch3 26159 dmdmd 27219 mdslmd1lem2 27245 sumdmdi 27339 dmdbr4ati 27340 dmdbr6ati 27342 gsumle 27770 gsumvsca1 27773 gsumvsca2 27774 pwsiga 28130 dfon2lem8 29222 meran1 29876 wl-syls2 29973 heibor1lem 30305 islinindfis 33050 con3ALT 33300 alrim3con13v 33304 bnj1533 33910 bnj110 33916 bnj1523 34127 bj-bi3ant 34178 bj-spnfw 34231 bj-spst 34242 bj-19.23bit 34244 bj-axrep2 34375 isltrn2N 35844 cdlemefrs32fva 36126 fiinfi 37758 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
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