Metamath Proof Explorer


Theorem ralprgOLD

Description: Obsolete version of ralprg as of 30-Sep-2024. (Contributed by NM, 17-Sep-2011) (Revised by Mario Carneiro, 23-Apr-2015) (Proof shortened by AV, 8-Apr-2023) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses ralprg.1 x = A φ ψ
ralprg.2 x = B φ χ
Assertion ralprgOLD A V B W x A B φ ψ χ

Proof

Step Hyp Ref Expression
1 ralprg.1 x = A φ ψ
2 ralprg.2 x = B φ χ
3 nfv x ψ
4 nfv x χ
5 3 4 1 2 ralprgf A V B W x A B φ ψ χ