Theorem parteq1

Description: Equality theorem for partition. (Contributed by Peter Mazsa, 5-Oct-2021)

	Ref	Expression
Assertion	parteq1	Could not format assertion : No typesetting found for |- ( R = S -> ( R Part A <-> S Part A ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		disjdmqseqeq1	$$⊢R=S\to \left(\left(DisjR\wedge \mathrm{dom}R/R=A\right)\leftrightarrow \left(DisjS\wedge \mathrm{dom}S/S=A\right)\right)$$
2		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 |-
3		dfpart2	Could not format ( S Part A <-> ( Disj S /\ ( dom S /. S ) = A ) ) : No typesetting found for |- ( S Part A <-> ( Disj S /\ ( dom S /. S ) = A ) ) with typecode |-
4	1 2 3	3bitr4g	Could not format ( R = S -> ( R Part A <-> S Part A ) ) : No typesetting found for |- ( R = S -> ( R Part A <-> S Part A ) ) with typecode |-