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Mirrors > Home > ILE Home > Th. List > ax-pre-mulext | Unicode version |
Description: Strong extensionality of
multiplication (expressed in terms of ![]() (Contributed by Jim Kingdon, 18-Feb-2020.) |
Ref | Expression |
---|---|
ax-pre-mulext |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . . 4
![]() ![]() | |
2 | cr 7798 |
. . . 4
![]() ![]() | |
3 | 1, 2 | wcel 2148 |
. . 3
![]() ![]() ![]() ![]() |
4 | cB |
. . . 4
![]() ![]() | |
5 | 4, 2 | wcel 2148 |
. . 3
![]() ![]() ![]() ![]() |
6 | cC |
. . . 4
![]() ![]() | |
7 | 6, 2 | wcel 2148 |
. . 3
![]() ![]() ![]() ![]() |
8 | 3, 5, 7 | w3a 978 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | cmul 7804 |
. . . . 5
![]() ![]() | |
10 | 1, 6, 9 | co 5869 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() |
11 | 4, 6, 9 | co 5869 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() |
12 | cltrr 7803 |
. . . 4
![]() ![]() | |
13 | 10, 11, 12 | wbr 4000 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 1, 4, 12 | wbr 4000 |
. . . 4
![]() ![]() ![]() ![]() |
15 | 4, 1, 12 | wbr 4000 |
. . . 4
![]() ![]() ![]() ![]() |
16 | 14, 15 | wo 708 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 13, 16 | wi 4 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 8, 17 | wi 4 |
1
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Colors of variables: wff set class |
This axiom is referenced by: remulext1 8543 |
Copyright terms: Public domain | W3C validator |