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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 7033 | . 2 |
4 | mulcomli.3 | . 2 | |
5 | 3, 4 | eqtri 2060 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 wcel 1393 (class class class)co 5512 cc 6887 cmul 6894 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-4 1400 ax-17 1419 ax-ext 2022 ax-mulcom 6985 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 |
This theorem is referenced by: nummul2c 8404 |
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