Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 3eqtr3i | GIF version |
Description: An inference from three chained equalities. (Contributed by NM, 6-May-1994.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
3eqtr3i.1 | ⊢ 𝐴 = 𝐵 |
3eqtr3i.2 | ⊢ 𝐴 = 𝐶 |
3eqtr3i.3 | ⊢ 𝐵 = 𝐷 |
Ref | Expression |
---|---|
3eqtr3i | ⊢ 𝐶 = 𝐷 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eqtr3i.1 | . . 3 ⊢ 𝐴 = 𝐵 | |
2 | 3eqtr3i.2 | . . 3 ⊢ 𝐴 = 𝐶 | |
3 | 1, 2 | eqtr3i 2062 | . 2 ⊢ 𝐵 = 𝐶 |
4 | 3eqtr3i.3 | . 2 ⊢ 𝐵 = 𝐷 | |
5 | 3, 4 | eqtr3i 2062 | 1 ⊢ 𝐶 = 𝐷 |
Colors of variables: wff set class |
Syntax hints: = wceq 1243 |
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 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 |
This theorem is referenced by: csbvarg 2877 un12 3101 in12 3148 indif1 3182 difundir 3190 difindir 3192 dif32 3200 resmpt3 4657 xp0 4743 fvsnun1 5360 caov12 5689 caov13 5691 rec1nq 6493 halfnqq 6508 negsubdii 7296 halfpm6th 8145 i4 9355 imi 9500 resqrexlemover 9608 |
Copyright terms: Public domain | W3C validator |