Theorem colleq1 41761

Description: Equality theorem for the collection operation. (Contributed by Rohan Ridenour, 11-Aug-2023.)

Assertion

Ref	Expression
colleq1	⊢ (𝐹 = 𝐺 → (𝐹 Coll 𝐴) = (𝐺 Coll 𝐴))

Proof of Theorem colleq1

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝐹 = 𝐺 → 𝐹 = 𝐺)
2		eqidd 2739	. 2 ⊢ (𝐹 = 𝐺 → 𝐴 = 𝐴)
3	1, 2	colleq12d 41760	1 ⊢ (𝐹 = 𝐺 → (𝐹 Coll 𝐴) = (𝐺 Coll 𝐴))

Syntax hints:   → wi 4   = wceq 1539   Coll ccoll 41757

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-3an 1087  df-tru 1542  df-fal 1552  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-ral 3068  df-rex 3069  df-rab 3072  df-v 3424  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4254  df-if 4457  df-sn 4559  df-pr 4561  df-op 4565  df-iun 4923  df-br 5071  df-opab 5133  df-cnv 5588  df-dm 5590  df-rn 5591  df-res 5592  df-ima 5593  df-scott 41743  df-coll 41758

This theorem is referenced by: (None)