Theorem bj-pr2eq

Description: Substitution property for pr2 . (Contributed by BJ, 6-Oct-2018)

	Ref	Expression
Assertion	bj-pr2eq	⊢ ( 𝐴 = 𝐵 → pr2 𝐴 = pr2 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		bj-projeq2	⊢ ( 𝐴 = 𝐵 → ( 1o Proj 𝐴 ) = ( 1o Proj 𝐵 ) )
2		df-bj-pr2	⊢ pr2 𝐴 = ( 1o Proj 𝐴 )
3		df-bj-pr2	⊢ pr2 𝐵 = ( 1o Proj 𝐵 )
4	1 2 3	3eqtr4g	⊢ ( 𝐴 = 𝐵 → pr2 𝐴 = pr2 𝐵 )