Theorem eceq2

Description: Equality theorem for equivalence class. (Contributed by NM, 23-Jul-1995)

	Ref	Expression
Assertion	eceq2	⊢ ( 𝐴 = 𝐵 → [ 𝐶 ] 𝐴 = [ 𝐶 ] 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		imaeq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 “ { 𝐶 } ) = ( 𝐵 “ { 𝐶 } ) )
2		df-ec	⊢ [ 𝐶 ] 𝐴 = ( 𝐴 “ { 𝐶 } )
3		df-ec	⊢ [ 𝐶 ] 𝐵 = ( 𝐵 “ { 𝐶 } )
4	1 2 3	3eqtr4g	⊢ ( 𝐴 = 𝐵 → [ 𝐶 ] 𝐴 = [ 𝐶 ] 𝐵 )