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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 7557 |
. 2
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4 | mulcomli.3 |
. 2
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5 | 3, 4 | eqtri 2109 |
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 ax-5 1382 ax-gen 1384 ax-4 1446 ax-17 1465 ax-ext 2071 ax-mulcom 7509 |
This theorem depends on definitions: df-bi 116 df-cleq 2082 |
This theorem is referenced by: nummul2c 8989 sq4e2t8 10115 cos2bnd 11114 ex-exp 11958 ex-fac 11959 |
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