Theorem mulsne0bd

Description: The product of two non-zero surreals is non-zero. (Contributed by Scott Fenton, 16-Apr-2025)

	Ref	Expression
Hypotheses	muls0ord.1	$$⊢\phi \to A\in \mathrm{No}$$
	muls0ord.2	$$⊢\phi \to B\in \mathrm{No}$$
Assertion	mulsne0bd	Could not format assertion : No typesetting found for |- ( ph -> ( ( A x.s B ) =/= 0s <-> ( A =/= 0s /\ B =/= 0s ) ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		muls0ord.1	$$⊢\phi \to A\in \mathrm{No}$$
2		muls0ord.2	$$⊢\phi \to B\in \mathrm{No}$$
3	1 2	muls0ord	Could not format ( ph -> ( ( A x.s B ) = 0s <-> ( A = 0s \/ B = 0s ) ) ) : No typesetting found for |- ( ph -> ( ( A x.s B ) = 0s <-> ( A = 0s \/ B = 0s ) ) ) with typecode |-
4	3	necon3abid	Could not format ( ph -> ( ( A x.s B ) =/= 0s <-> -. ( A = 0s \/ B = 0s ) ) ) : No typesetting found for |- ( ph -> ( ( A x.s B ) =/= 0s <-> -. ( A = 0s \/ B = 0s ) ) ) with typecode |-
5		neanior	Could not format ( ( A =/= 0s /\ B =/= 0s ) <-> -. ( A = 0s \/ B = 0s ) ) : No typesetting found for |- ( ( A =/= 0s /\ B =/= 0s ) <-> -. ( A = 0s \/ B = 0s ) ) with typecode |-
6	4 5	bitr4di	Could not format ( ph -> ( ( A x.s B ) =/= 0s <-> ( A =/= 0s /\ B =/= 0s ) ) ) : No typesetting found for |- ( ph -> ( ( A x.s B ) =/= 0s <-> ( A =/= 0s /\ B =/= 0s ) ) ) with typecode |-