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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 | |
axi.2 | |
mulcomli.3 |
Ref | Expression |
---|---|
mulcomli |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axi.2 | . . 3 | |
2 | axi.1 | . . 3 | |
3 | 1, 2 | mulcomi 7926 | . 2 |
4 | mulcomli.3 | . 2 | |
5 | 3, 4 | eqtri 2191 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1348 wcel 2141 (class class class)co 5853 cc 7772 cmul 7779 |
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 1440 ax-gen 1442 ax-4 1503 ax-17 1519 ax-ext 2152 ax-mulcom 7875 |
This theorem depends on definitions: df-bi 116 df-cleq 2163 |
This theorem is referenced by: nummul2c 9392 halfthird 9485 5recm6rec 9486 sq4e2t8 10573 cos2bnd 11723 ex-exp 13762 ex-fac 13763 |
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