Theorem divsclwd

Description: Weak division closure law. (Contributed by Scott Fenton, 12-Mar-2025)

	Ref	Expression
Hypotheses	divsclwd.1	$$⊢\phi \to A\in \mathrm{No}$$
	divsclwd.2	$$⊢\phi \to B\in \mathrm{No}$$
	divsclwd.3	No typesetting found for |- ( ph -> B =/= 0s ) with typecode |-
	divsclwd.4	No typesetting found for |- ( ph -> E. x e. No ( B x.s x ) = 1s ) with typecode |-
Assertion	divsclwd	Could not format assertion : No typesetting found for |- ( ph -> ( A /su B ) e. No ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		divsclwd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		divsclwd.2	$$⊢\phi \to B\in \mathrm{No}$$
3		divsclwd.3	Could not format ( ph -> B =/= 0s ) : No typesetting found for |- ( ph -> B =/= 0s ) with typecode |-
4		divsclwd.4	Could not format ( ph -> E. x e. No ( B x.s x ) = 1s ) : No typesetting found for |- ( ph -> E. x e. No ( B x.s x ) = 1s ) with typecode |-
5		divsclw	Could not format ( ( ( A e. No /\ B e. No /\ B =/= 0s ) /\ E. x e. No ( B x.s x ) = 1s ) -> ( A /su B ) e. No ) : No typesetting found for |- ( ( ( A e. No /\ B e. No /\ B =/= 0s ) /\ E. x e. No ( B x.s x ) = 1s ) -> ( A /su B ) e. No ) with typecode |-
6	1 2 3 4 5	syl31anc	Could not format ( ph -> ( A /su B ) e. No ) : No typesetting found for |- ( ph -> ( A /su B ) e. No ) with typecode |-