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Mirrors > Home > NFE Home > Th. List > 3eqtr3ri | GIF version |
Description: An inference from three chained equalities. (Contributed by NM, 15-Aug-2004.) |
Ref | Expression |
---|---|
3eqtr3i.1 | ⊢ A = B |
3eqtr3i.2 | ⊢ A = C |
3eqtr3i.3 | ⊢ B = D |
Ref | Expression |
---|---|
3eqtr3ri | ⊢ D = C |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3eqtr3i.3 | . 2 ⊢ B = D | |
2 | 3eqtr3i.1 | . . 3 ⊢ A = B | |
3 | 3eqtr3i.2 | . . 3 ⊢ A = C | |
4 | 2, 3 | eqtr3i 2375 | . 2 ⊢ B = C |
5 | 1, 4 | eqtr3i 2375 | 1 ⊢ D = C |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1642 |
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: indif2 3498 dfif5 3674 nchoicelem2 6290 |
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