Theorem muls4d

Description: Rearrangement of four surreal factors. (Contributed by Scott Fenton, 16-Apr-2025)

	Ref	Expression
Hypotheses	muls4d.1	$$⊢\phi \to A\in \mathrm{No}$$
	muls4d.2	$$⊢\phi \to B\in \mathrm{No}$$
	muls4d.3	$$⊢\phi \to C\in \mathrm{No}$$
	muls4d.4	$$⊢\phi \to D\in \mathrm{No}$$
Assertion	muls4d	Could not format assertion : No typesetting found for |- ( ph -> ( ( A x.s B ) x.s ( C x.s D ) ) = ( ( A x.s C ) x.s ( B x.s D ) ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		muls4d.1	$$⊢\phi \to A\in \mathrm{No}$$
2		muls4d.2	$$⊢\phi \to B\in \mathrm{No}$$
3		muls4d.3	$$⊢\phi \to C\in \mathrm{No}$$
4		muls4d.4	$$⊢\phi \to D\in \mathrm{No}$$
5	2 3	mulscomd	Could not format ( ph -> ( B x.s C ) = ( C x.s B ) ) : No typesetting found for |- ( ph -> ( B x.s C ) = ( C x.s B ) ) with typecode |-
6	5	oveq1d	Could not format ( ph -> ( ( B x.s C ) x.s D ) = ( ( C x.s B ) x.s D ) ) : No typesetting found for |- ( ph -> ( ( B x.s C ) x.s D ) = ( ( C x.s B ) x.s D ) ) with typecode |-
7	2 3 4	mulsassd	Could not format ( ph -> ( ( B x.s C ) x.s D ) = ( B x.s ( C x.s D ) ) ) : No typesetting found for |- ( ph -> ( ( B x.s C ) x.s D ) = ( B x.s ( C x.s D ) ) ) with typecode |-
8	3 2 4	mulsassd	Could not format ( ph -> ( ( C x.s B ) x.s D ) = ( C x.s ( B x.s D ) ) ) : No typesetting found for |- ( ph -> ( ( C x.s B ) x.s D ) = ( C x.s ( B x.s D ) ) ) with typecode |-
9	6 7 8	3eqtr3d	Could not format ( ph -> ( B x.s ( C x.s D ) ) = ( C x.s ( B x.s D ) ) ) : No typesetting found for |- ( ph -> ( B x.s ( C x.s D ) ) = ( C x.s ( B x.s D ) ) ) with typecode |-
10	9	oveq2d	Could not format ( ph -> ( A x.s ( B x.s ( C x.s D ) ) ) = ( A x.s ( C x.s ( B x.s D ) ) ) ) : No typesetting found for |- ( ph -> ( A x.s ( B x.s ( C x.s D ) ) ) = ( A x.s ( C x.s ( B x.s D ) ) ) ) with typecode |-
11	3 4	mulscld	Could not format ( ph -> ( C x.s D ) e. No ) : No typesetting found for |- ( ph -> ( C x.s D ) e. No ) with typecode |-
12	1 2 11	mulsassd	Could not format ( ph -> ( ( A x.s B ) x.s ( C x.s D ) ) = ( A x.s ( B x.s ( C x.s D ) ) ) ) : No typesetting found for |- ( ph -> ( ( A x.s B ) x.s ( C x.s D ) ) = ( A x.s ( B x.s ( C x.s D ) ) ) ) with typecode |-
13	2 4	mulscld	Could not format ( ph -> ( B x.s D ) e. No ) : No typesetting found for |- ( ph -> ( B x.s D ) e. No ) with typecode |-
14	1 3 13	mulsassd	Could not format ( ph -> ( ( A x.s C ) x.s ( B x.s D ) ) = ( A x.s ( C x.s ( B x.s D ) ) ) ) : No typesetting found for |- ( ph -> ( ( A x.s C ) x.s ( B x.s D ) ) = ( A x.s ( C x.s ( B x.s D ) ) ) ) with typecode |-
15	10 12 14	3eqtr4d	Could not format ( ph -> ( ( A x.s B ) x.s ( C x.s D ) ) = ( ( A x.s C ) x.s ( B x.s D ) ) ) : No typesetting found for |- ( ph -> ( ( A x.s B ) x.s ( C x.s D ) ) = ( ( A x.s C ) x.s ( B x.s D ) ) ) with typecode |-