Theorem coideq 38747

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 5829	. 2 ⊢ (𝐴 = 𝐵 → (𝐴 ∘ 𝐴) = (𝐵 ∘ 𝐴))
2		coeq2 5830	. 2 ⊢ (𝐴 = 𝐵 → (𝐵 ∘ 𝐴) = (𝐵 ∘ 𝐵))
3	1, 2	eqtrd 2797	1 ⊢ (𝐴 = 𝐵 → (𝐴 ∘ 𝐴) = (𝐵 ∘ 𝐵))

Syntax hints:   → wi 4   = wceq 1560   ∘ ccom 5651

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-ext 2734

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1800  df-sb 2091  df-clab 2741  df-cleq 2754  df-clel 2837  df-ss 3921  df-br 5101  df-opab 5163  df-co 5656

This theorem is referenced by:  eltrrels2  39162  trreleq  39165  eleqvrels2  39175