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Mirrors > Home > ILE Home > Th. List > bicom | Unicode version |
Description: Commutative law for equivalence. Theorem *4.21 of [WhiteheadRussell] p. 117. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 11-Nov-2012.) |
Ref | Expression |
---|---|
bicom |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bicom1 130 |
. 2
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2 | bicom1 130 |
. 2
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3 | 1, 2 | impbii 125 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: bicomd 140 bibi1i 227 bibi1d 232 ibibr 245 bibif 655 con2bidc 813 con2biddc 818 pm5.17dc 854 bigolden 907 nbbndc 1340 bilukdc 1342 falbitru 1363 3impexpbicom 1382 exists1 2056 eqcom 2102 abeq1 2209 necon2abiddc 2333 necon2bbiddc 2334 necon4bbiddc 2341 ssequn1 3193 axpow3 4041 isocnv 5644 uzennn 10050 bezoutlemle 11489 |
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