Metamath Proof Explorer


Theorem ccat2s1fstOLD

Description: Obsolete version of ccat2s1fst as of 28-Jan-2024. The first symbol of the concatenation of a word with two single symbols. (Contributed by Alexander van der Vekens, 22-Sep-2018) (New usage is discouraged.) (Proof modification is discouraged.)

Ref Expression
Assertion ccat2s1fstOLD
|- ( ( ( W e. Word V /\ 0 < ( # ` W ) ) /\ ( X e. V /\ Y e. V ) ) -> ( ( ( W ++ <" X "> ) ++ <" Y "> ) ` 0 ) = ( W ` 0 ) )

Proof

Step Hyp Ref Expression
1 0nn0
 |-  0 e. NN0
2 ccat2s1fvwOLD
 |-  ( ( ( W e. Word V /\ 0 e. NN0 /\ 0 < ( # ` W ) ) /\ ( X e. V /\ Y e. V ) ) -> ( ( ( W ++ <" X "> ) ++ <" Y "> ) ` 0 ) = ( W ` 0 ) )
3 1 2 mp3anl2
 |-  ( ( ( W e. Word V /\ 0 < ( # ` W ) ) /\ ( X e. V /\ Y e. V ) ) -> ( ( ( W ++ <" X "> ) ++ <" Y "> ) ` 0 ) = ( W ` 0 ) )