Theorem colleq2 44852

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

Step	Hyp	Ref	Expression
1		eqidd 2770	. 2 ⊢ (𝐴 = 𝐵 → 𝐹 = 𝐹)
2		id 23	. 2 ⊢ (𝐴 = 𝐵 → 𝐴 = 𝐵)
3	1, 2	colleq12d 44850	1 ⊢ (𝐴 = 𝐵 → (𝐹 Coll 𝐴) = (𝐹 Coll 𝐵))

Syntax hints:   → wi 4   = wceq 1567   Coll ccoll 44847

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1103  df-tru 1570  df-fal 1580  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-ral 3086  df-rex 3096  df-rab 3424  df-v 3465  df-dif 3916  df-un 3918  df-in 3920  df-ss 3930  df-nul 4295  df-if 4490  df-sn 4592  df-pr 4594  df-op 4598  df-iun 4959  df-br 5111  df-opab 5175  df-cnv 5667  df-dm 5669  df-rn 5670  df-res 5671  df-ima 5672  df-scott 9854  df-coll 44848

This theorem is referenced by: (None)