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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 7765 | . 2 |
4 | mulcomli.3 | . 2 | |
5 | 3, 4 | eqtri 2158 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 wcel 1480 (class class class)co 5767 cc 7611 cmul 7618 |
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 1423 ax-gen 1425 ax-4 1487 ax-17 1506 ax-ext 2119 ax-mulcom 7714 |
This theorem depends on definitions: df-bi 116 df-cleq 2130 |
This theorem is referenced by: nummul2c 9224 halfthird 9317 5recm6rec 9318 sq4e2t8 10383 cos2bnd 11456 ex-exp 12928 ex-fac 12929 |
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