Theorem coideq 36312

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 5755	. 2 ⊢ (𝐴 = 𝐵 → (𝐴 ∘ 𝐴) = (𝐵 ∘ 𝐴))
2		coeq2 5756	. 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 5584

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-tru 1542  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-in 3890  df-ss 3900  df-br 5071  df-opab 5133  df-co 5589

This theorem is referenced by:  eltrrels2  36620  trreleq  36623  eleqvrels2  36632