Theorem eqeltr

Description: Substitution of equal classes into elementhood relation. (Contributed by Peter Mazsa, 22-Jul-2017)

	Ref	Expression
Assertion	eqeltr	$$⊢\left(A=B\wedge B\in C\right)\to A\in C$$

Proof

Step	Hyp	Ref	Expression
1		eleq1	$$⊢A=B\to \left(A\in C\leftrightarrow B\in C\right)$$
2	1	biimpar	$$⊢\left(A=B\wedge B\in C\right)\to A\in C$$