Theorem bj-pr1eq

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

	Ref	Expression
Assertion	bj-pr1eq	⊢ ( 𝐴 = 𝐵 → pr1 𝐴 = pr1 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		bj-projeq2	⊢ ( 𝐴 = 𝐵 → ( ∅ Proj 𝐴 ) = ( ∅ Proj 𝐵 ) )
2		df-bj-pr1	⊢ pr1 𝐴 = ( ∅ Proj 𝐴 )
3		df-bj-pr1	⊢ pr1 𝐵 = ( ∅ Proj 𝐵 )
4	1 2 3	3eqtr4g	⊢ ( 𝐴 = 𝐵 → pr1 𝐴 = pr1 𝐵 )