Theorem adds42d

Description: Rearrangement of four terms in a surreal sum. (Contributed by Scott Fenton, 5-Feb-2025)

	Ref	Expression
Hypotheses	adds4d.1	$$⊢\phi \to A\in \mathrm{No}$$
	adds4d.2	$$⊢\phi \to B\in \mathrm{No}$$
	adds4d.3	$$⊢\phi \to C\in \mathrm{No}$$
	adds4d.4	$$⊢\phi \to D\in \mathrm{No}$$
Assertion	adds42d	Could not format assertion : No typesetting found for |- ( ph -> ( ( A +s B ) +s ( C +s D ) ) = ( ( A +s C ) +s ( D +s B ) ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		adds4d.1	$$⊢\phi \to A\in \mathrm{No}$$
2		adds4d.2	$$⊢\phi \to B\in \mathrm{No}$$
3		adds4d.3	$$⊢\phi \to C\in \mathrm{No}$$
4		adds4d.4	$$⊢\phi \to D\in \mathrm{No}$$
5	1 2 3 4	adds4d	Could not format ( ph -> ( ( A +s B ) +s ( C +s D ) ) = ( ( A +s C ) +s ( B +s D ) ) ) : No typesetting found for |- ( ph -> ( ( A +s B ) +s ( C +s D ) ) = ( ( A +s C ) +s ( B +s D ) ) ) with typecode |-
6	2 4	addscomd	Could not format ( ph -> ( B +s D ) = ( D +s B ) ) : No typesetting found for |- ( ph -> ( B +s D ) = ( D +s B ) ) with typecode |-
7	6	oveq2d	Could not format ( ph -> ( ( A +s C ) +s ( B +s D ) ) = ( ( A +s C ) +s ( D +s B ) ) ) : No typesetting found for |- ( ph -> ( ( A +s C ) +s ( B +s D ) ) = ( ( A +s C ) +s ( D +s B ) ) ) with typecode |-
8	5 7	eqtrd	Could not format ( ph -> ( ( A +s B ) +s ( C +s D ) ) = ( ( A +s C ) +s ( D +s B ) ) ) : No typesetting found for |- ( ph -> ( ( A +s B ) +s ( C +s D ) ) = ( ( A +s C ) +s ( D +s B ) ) ) with typecode |-