Theorem sylan9req

Description: An equality transitivity deduction. (Contributed by NM, 23-Jun-2007)

	Ref	Expression
Hypotheses	sylan9req.1	$$⊢\phi \to B=A$$
	sylan9req.2	$$⊢\psi \to B=C$$
Assertion	sylan9req	$$⊢\left(\phi \wedge \psi \right)\to A=C$$

Proof

Step	Hyp	Ref	Expression
1		sylan9req.1	$$⊢\phi \to B=A$$
2		sylan9req.2	$$⊢\psi \to B=C$$
3	1	eqcomd	$$⊢\phi \to A=B$$
4	3 2	sylan9eq	$$⊢\left(\phi \wedge \psi \right)\to A=C$$