Theorem ifeq1d

Description: Equality deduction for conditional operator. (Contributed by NM, 16-Feb-2005)

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

Proof

Step	Hyp	Ref	Expression
1		ifeq1d.1	$$⊢\phi \to A=B$$
2		ifeq1	$$⊢A=B\to if\left(\psi ,A,C\right)=if\left(\psi ,B,C\right)$$
3	1 2	syl	$$⊢\phi \to if\left(\psi ,A,C\right)=if\left(\psi ,B,C\right)$$