Theorem eqeq12

Description: Equality relationship among four classes. (Contributed by NM, 3-Aug-1994)

	Ref	Expression
Assertion	eqeq12	$$⊢\left(A=B\wedge C=D\right)\to \left(A=C\leftrightarrow B=D\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqeq1	$$⊢A=B\to \left(A=C\leftrightarrow B=C\right)$$
2		eqeq2	$$⊢C=D\to \left(B=C\leftrightarrow B=D\right)$$
3	1 2	sylan9bb	$$⊢\left(A=B\wedge C=D\right)\to \left(A=C\leftrightarrow B=D\right)$$