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Theorem colleq2 42477
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 2737 . 2 (𝐴 = 𝐵𝐹 = 𝐹)
2 id 22 . 2 (𝐴 = 𝐵𝐴 = 𝐵)
31, 2colleq12d 42475 1 (𝐴 = 𝐵 → (𝐹 Coll 𝐴) = (𝐹 Coll 𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1541   Coll ccoll 42472
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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-ral 3063  df-rex 3072  df-rab 3406  df-v 3445  df-dif 3911  df-un 3913  df-in 3915  df-ss 3925  df-nul 4281  df-if 4485  df-sn 4585  df-pr 4587  df-op 4591  df-iun 4954  df-br 5104  df-opab 5166  df-cnv 5639  df-dm 5641  df-rn 5642  df-res 5643  df-ima 5644  df-scott 42458  df-coll 42473
This theorem is referenced by: (None)
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