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Mirrors > Home > ILE Home > Th. List > biimprcd | Unicode version |
Description: Deduce a converse commuted implication from a logical equivalence. (Contributed by NM, 3-May-1994.) (Proof shortened by Wolf Lammen, 20-Dec-2013.) |
Ref | Expression |
---|---|
biimpcd.1 |
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Ref | Expression |
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biimprcd |
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Step | Hyp | Ref | Expression |
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1 | id 19 |
. 2
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2 | biimpcd.1 |
. 2
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3 | 1, 2 | syl5ibrcom 157 |
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: biimparc 299 pm5.32 453 oplem1 975 ax11i 1714 equsex 1728 eleq1a 2249 ceqsalg 2767 cgsexg 2774 cgsex2g 2775 cgsex4g 2776 ceqsex 2777 spc2egv 2829 spc3egv 2831 csbiebt 3098 dfiin2g 3921 sotricim 4325 ralxfrALT 4469 iunpw 4482 opelxp 4658 ssrel 4716 ssrel2 4718 ssrelrel 4728 iss 4955 funcnvuni 5287 fun11iun 5484 tfrlem8 6321 eroveu 6628 fundmen 6808 nneneq 6859 fidifsnen 6872 prarloclem5 7501 prarloc 7504 recexprlemss1l 7636 recexprlemss1u 7637 uzin 9562 indstr 9595 elfzmlbp 10134 |
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