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Theorem disjwrdpfx 41918
Description: Sets of words are disjoint if each set contains extensions of distinct words of a fixed length. Could replace disjxwrd 13655. (Contributed by AV, 6-May-2020.)
Assertion
Ref Expression
disjwrdpfx Disj 𝑦𝑊 {𝑥 ∈ Word 𝑉 ∣ (𝑥 prefix 𝑁) = 𝑦}
Distinct variable groups:   𝑦,𝑁   𝑥,𝑉   𝑥,𝑦
Allowed substitution hints:   𝑁(𝑥)   𝑉(𝑦)   𝑊(𝑥,𝑦)

Proof of Theorem disjwrdpfx
StepHypRef Expression
1 invdisjrab 4791 1 Disj 𝑦𝑊 {𝑥 ∈ Word 𝑉 ∣ (𝑥 prefix 𝑁) = 𝑦}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1632  {crab 3054  Disj wdisj 4772  (class class class)co 6813  Word cword 13477   prefix cpfx 41891
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-eu 2611  df-mo 2612  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-ral 3055  df-rmo 3058  df-rab 3059  df-v 3342  df-sbc 3577  df-csb 3675  df-disj 4773
This theorem is referenced by: (None)
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