Metamath Proof Explorer


Theorem mulscld

Description: The surreals are closed under multiplication. Theorem 8(i) of Conway p. 19. (Contributed by Scott Fenton, 6-Mar-2025)

Ref Expression
Hypotheses mulscld.1 φ A No
mulscld.2 φ B No
Assertion mulscld φ A s B No

Proof

Step Hyp Ref Expression
1 mulscld.1 φ A No
2 mulscld.2 φ B No
3 mulscl A No B No A s B No
4 1 2 3 syl2anc φ A s B No