Theorem sylan9eqr

Description: An equality transitivity deduction. (Contributed by NM, 8-May-1994)

	Ref	Expression
Hypotheses	sylan9eqr.1	$$⊢\phi \to A=B$$
	sylan9eqr.2	$$⊢\psi \to B=C$$
Assertion	sylan9eqr	$$⊢\left(\psi \wedge \phi \right)\to A=C$$

Proof

Step	Hyp	Ref	Expression
1		sylan9eqr.1	$$⊢\phi \to A=B$$
2		sylan9eqr.2	$$⊢\psi \to B=C$$
3	1 2	sylan9eq	$$⊢\left(\phi \wedge \psi \right)\to A=C$$
4	3	ancoms	$$⊢\left(\psi \wedge \phi \right)\to A=C$$