Metamath Proof Explorer


Theorem rmoeq1OLD

Description: Obsolete version of rmoeq1 as of 12-Mar-2025. (Contributed by Alexander van der Vekens, 17-Jun-2017) Remove usage of ax-10 , ax-11 , and ax-12 . (Revised by Steven Nguyen, 30-Apr-2023) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion rmoeq1OLD A = B * x A φ * x B φ

Proof

Step Hyp Ref Expression
1 eleq2 A = B x A x B
2 1 anbi1d A = B x A φ x B φ
3 2 mobidv A = B * x x A φ * x x B φ
4 df-rmo * x A φ * x x A φ
5 df-rmo * x B φ * x x B φ
6 3 4 5 3bitr4g A = B * x A φ * x B φ