Theorem parteq2

Description: Equality theorem for partition. (Contributed by Peter Mazsa, 25-Jul-2024)

	Ref	Expression
Assertion	parteq2	Could not format assertion : No typesetting found for |- ( A = B -> ( R Part A <-> R Part B ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		eqeq2	$$⊢A=B\to \left(\mathrm{dom}R/R=A\leftrightarrow \mathrm{dom}R/R=B\right)$$
2	1	anbi2d	$$⊢A=B\to \left(\left(DisjR\wedge \mathrm{dom}R/R=A\right)\leftrightarrow \left(DisjR\wedge \mathrm{dom}R/R=B\right)\right)$$
3		dfpart2	Could not format ( R Part A <-> ( Disj R /\ ( dom R /. R ) = A ) ) : No typesetting found for |- ( R Part A <-> ( Disj R /\ ( dom R /. R ) = A ) ) with typecode |-
4		dfpart2	Could not format ( R Part B <-> ( Disj R /\ ( dom R /. R ) = B ) ) : No typesetting found for |- ( R Part B <-> ( Disj R /\ ( dom R /. R ) = B ) ) with typecode |-
5	2 3 4	3bitr4g	Could not format ( A = B -> ( R Part A <-> R Part B ) ) : No typesetting found for |- ( A = B -> ( R Part A <-> R Part B ) ) with typecode |-