Metamath Proof Explorer


Theorem bj-inrab2

Description: Shorter proof of inrab . (Contributed by BJ, 21-Apr-2019) (Proof modification is discouraged.)

Ref Expression
Assertion bj-inrab2 x A | φ x A | ψ = x A | φ ψ

Proof

Step Hyp Ref Expression
1 bj-inrab x A | φ x A | ψ = x A A | φ ψ
2 nfv x
3 inidm A A = A
4 3 a1i A A = A
5 2 4 bj-rabeqd x A A | φ ψ = x A | φ ψ
6 5 mptru x A A | φ ψ = x A | φ ψ
7 1 6 eqtri x A | φ x A | ψ = x A | φ ψ