![]() |
New Foundations Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > NFE Home > Th. List > 3eqtrd | Unicode version |
Description: A deduction from three chained equalities. (Contributed by NM, 29-Oct-1995.) |
Ref | Expression |
---|---|
3eqtrd.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3eqtrd.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3eqtrd.3 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
3eqtrd |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eqtrd.1 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 3eqtrd.2 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 3eqtrd.3 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 2, 3 | eqtrd 2385 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 1, 4 | eqtrd 2385 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-ex 1542 df-cleq 2346 |
This theorem is referenced by: tpeq123d 3815 diftpsn3 3850 vfinncsp 4555 fvun 5379 oveq123d 5544 fvmptd 5703 |
Copyright terms: Public domain | W3C validator |