Theorem coideq 36385

Description: Equality theorem for composition of two classes. (Contributed by Peter Mazsa, 23-Sep-2021.)

Assertion

Ref	Expression
coideq	⊢ (𝐴 = 𝐵 → (𝐴 ∘ 𝐴) = (𝐵 ∘ 𝐵))

Proof of Theorem coideq

Step	Hyp	Ref	Expression
1		coeq1 5766	. 2 ⊢ (𝐴 = 𝐵 → (𝐴 ∘ 𝐴) = (𝐵 ∘ 𝐴))
2		coeq2 5767	. 2 ⊢ (𝐴 = 𝐵 → (𝐵 ∘ 𝐴) = (𝐵 ∘ 𝐵))
3	1, 2	eqtrd 2778	1 ⊢ (𝐴 = 𝐵 → (𝐴 ∘ 𝐴) = (𝐵 ∘ 𝐵))

Syntax hints:   → wi 4   = wceq 1539   ∘ ccom 5593

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-in 3894  df-ss 3904  df-br 5075  df-opab 5137  df-co 5598

This theorem is referenced by:  eltrrels2  36693  trreleq  36696  eleqvrels2  36705