Theorem ifeq12d

Description: Equality deduction for conditional operator. (Contributed by NM, 24-Mar-2015)

	Ref	Expression
Hypotheses	ifeq1d.1	$$⊢\phi \to A=B$$
	ifeq12d.2	$$⊢\phi \to C=D$$
Assertion	ifeq12d	$$⊢\phi \to if\left(\psi ,A,C\right)=if\left(\psi ,B,D\right)$$

Proof

Step	Hyp	Ref	Expression
1		ifeq1d.1	$$⊢\phi \to A=B$$
2		ifeq12d.2	$$⊢\phi \to C=D$$
3	1	ifeq1d	$$⊢\phi \to if\left(\psi ,A,C\right)=if\left(\psi ,B,C\right)$$
4	2	ifeq2d	$$⊢\phi \to if\left(\psi ,B,C\right)=if\left(\psi ,B,D\right)$$
5	3 4	eqtrd	$$⊢\phi \to if\left(\psi ,A,C\right)=if\left(\psi ,B,D\right)$$