Theorem bj-pr1eq

Description: Substitution property for pr1 . (Contributed by BJ, 6-Apr-2019)

	Ref	Expression
Assertion	bj-pr1eq	$$⊢A=B\to pr1A=pr1B$$

Proof

Step	Hyp	Ref	Expression
1		bj-projeq2	$$⊢A=B\to \left(\varnothing ProjA\right)=\left(\varnothing ProjB\right)$$
2		df-bj-pr1	$$⊢pr1A=\left(\varnothing ProjA\right)$$
3		df-bj-pr1	$$⊢pr1B=\left(\varnothing ProjB\right)$$
4	1 2 3	3eqtr4g	$$⊢A=B\to pr1A=pr1B$$