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Mirrors > Home > ILE Home > Th. List > mulcomli | Unicode version |
Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.) |
Ref | Expression |
---|---|
axi.1 |
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axi.2 |
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mulcomli.3 |
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Ref | Expression |
---|---|
mulcomli |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axi.2 |
. . 3
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2 | axi.1 |
. . 3
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3 | 1, 2 | mulcomi 7796 |
. 2
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4 | mulcomli.3 |
. 2
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5 | 3, 4 | eqtri 2161 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-4 1488 ax-17 1507 ax-ext 2122 ax-mulcom 7745 |
This theorem depends on definitions: df-bi 116 df-cleq 2133 |
This theorem is referenced by: nummul2c 9255 halfthird 9348 5recm6rec 9349 sq4e2t8 10421 cos2bnd 11503 ex-exp 13110 ex-fac 13111 |
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