Description: The first symbol of the concatenation of a word with two single symbols. (Contributed by Alexander van der Vekens, 22-Sep-2018) (Revised by AV, 28-Jan-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | ccat2s1fst | |- ( ( W e. Word V /\ 0 < ( # ` W ) ) -> ( ( ( W ++ <" X "> ) ++ <" Y "> ) ` 0 ) = ( W ` 0 ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 0nn0 | |- 0 e. NN0 |
|
| 2 | ccat2s1fvw | |- ( ( W e. Word V /\ 0 e. NN0 /\ 0 < ( # ` W ) ) -> ( ( ( W ++ <" X "> ) ++ <" Y "> ) ` 0 ) = ( W ` 0 ) ) |
|
| 3 | 1 2 | mp3an2 | |- ( ( W e. Word V /\ 0 < ( # ` W ) ) -> ( ( ( W ++ <" X "> ) ++ <" Y "> ) ` 0 ) = ( W ` 0 ) ) |