Metamath Proof Explorer


Theorem ralcom13OLD

Description: Obsolete version of ralcom13 as of 2-Jan-2025. (Contributed by AV, 3-Dec-2021) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion ralcom13OLD x A y B z C φ z C y B x A φ

Proof

Step Hyp Ref Expression
1 ralcom x A y B z C φ y B x A z C φ
2 ralcom x A z C φ z C x A φ
3 2 ralbii y B x A z C φ y B z C x A φ
4 ralcom y B z C x A φ z C y B x A φ
5 1 3 4 3bitri x A y B z C φ z C y B x A φ