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Theorem colleq2 40883
Description: Equality theorem for the collection operation. (Contributed by Rohan Ridenour, 11-Aug-2023.)
Assertion
Ref Expression
colleq2 (𝐴 = 𝐵 → (𝐹 Coll 𝐴) = (𝐹 Coll 𝐵))

Proof of Theorem colleq2
StepHypRef Expression
1 eqidd 2825 . 2 (𝐴 = 𝐵𝐹 = 𝐹)
2 id 22 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2colleq12d 40881 1 (𝐴 = 𝐵 → (𝐹 Coll 𝐴) = (𝐹 Coll 𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1538   Coll ccoll 40878
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-rex 3139  df-rab 3142  df-v 3482  df-un 3924  df-in 3926  df-ss 3936  df-sn 4551  df-pr 4553  df-op 4557  df-iun 4907  df-br 5053  df-opab 5115  df-cnv 5550  df-dm 5552  df-rn 5553  df-res 5554  df-ima 5555  df-scott 40864  df-coll 40879
This theorem is referenced by: (None)
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