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Mirrors > Home > ILE Home > Th. List > imbi2i | Unicode version |
Description: Introduce an antecedent to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 6-Feb-2013.) |
Ref | Expression |
---|---|
bi.a |
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Ref | Expression |
---|---|
imbi2i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi.a |
. . 3
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2 | 1 | a1i 9 |
. 2
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3 | 2 | pm5.74i 180 |
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: imbi12i 239 anidmdbi 398 nan 692 sbcof2 1810 sblimv 1894 sbhb 1940 sblim 1957 2sb6 1984 sbcom2v 1985 2sb6rf 1990 eu1 2051 moabs 2075 mo3h 2079 moanim 2100 2moswapdc 2116 r2alf 2494 r19.21t 2552 rspc2gv 2853 reu2 2925 reu8 2933 2reuswapdc 2941 2rmorex 2943 dfdif3 3245 ssconb 3268 ssin 3357 reldisj 3474 ssundifim 3506 ralm 3527 unissb 3839 repizf2lem 4161 elirr 4540 en2lp 4553 tfi 4581 ssrel 4714 ssrel2 4716 fncnv 5282 fun11 5283 axcaucvglemres 7897 axpre-suploc 7900 suprzclex 9350 raluz2 9578 supinfneg 9594 infsupneg 9595 infssuzex 11949 bezoutlemmain 11998 isprm2 12116 lmres 13718 limcdifap 14101 |
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