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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 7966 |
. 2
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4 | mulcomli.3 |
. 2
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5 | 3, 4 | eqtri 2198 |
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 ax-5 1447 ax-gen 1449 ax-4 1510 ax-17 1526 ax-ext 2159 ax-mulcom 7915 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 |
This theorem is referenced by: nummul2c 9436 halfthird 9529 5recm6rec 9530 sq4e2t8 10621 cos2bnd 11771 2lgsoddprmlem3c 14618 2lgsoddprmlem3d 14619 ex-exp 14640 ex-fac 14641 |
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