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Mirrors > Home > ILE Home > Th. List > imbi1i | Unicode version |
Description: Introduce a consequent to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 17-Sep-2013.) |
Ref | Expression |
---|---|
imbi1i.1 |
Ref | Expression |
---|---|
imbi1i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imbi1i.1 | . 2 | |
2 | imbi1 235 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: imbi12i 238 ancomsimp 1416 sbrim 1929 sbal1yz 1976 sbmo 2058 mo4f 2059 moanim 2073 necon4addc 2378 necon1bddc 2385 nfraldya 2469 r3al 2477 r19.23t 2539 ceqsralt 2713 ralab 2844 ralrab 2845 euind 2871 reu2 2872 rmo4 2877 rmo3f 2881 rmo4f 2882 reuind 2889 rmo3 3000 dfdif3 3186 raldifb 3216 unss 3250 ralunb 3257 inssdif0im 3430 ssundifim 3446 raaan 3469 pwss 3526 ralsnsg 3561 ralsns 3562 disjsn 3585 snss 3649 unissb 3766 intun 3802 intpr 3803 dfiin2g 3846 dftr2 4028 repizf2lem 4085 axpweq 4095 zfpow 4099 axpow2 4100 zfun 4356 uniex2 4358 setindel 4453 setind 4454 elirr 4456 en2lp 4469 zfregfr 4488 tfi 4496 raliunxp 4680 dffun2 5133 dffun4 5134 dffun4f 5139 dffun7 5150 funcnveq 5186 fununi 5191 fiintim 6817 addnq0mo 7255 mulnq0mo 7256 addsrmo 7551 mulsrmo 7552 prime 9150 raluz2 9374 ralrp 9463 modfsummod 11227 isprm4 11800 dedekindicclemicc 12779 bdcriota 13081 bj-uniex2 13114 bj-ssom 13134 |
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