Theorem ranrcl4lem

Description: Lemma for ranrcl4 and ranrcl5 . (Contributed by Zhi Wang, 4-Nov-2025)

	Ref	Expression
Hypothesis	ranrcl2.l	No typesetting found for |- ( ph -> L ( F ( <. C , D >. Ran E ) X ) A ) with typecode |-
Assertion	ranrcl4lem	Could not format assertion : No typesetting found for |- ( ph -> ( <. D , E >. -o.F F ) = <. ( 1st ` ( <. D , E >. -o.F F ) ) , ( 2nd ` ( <. D , E >. -o.F F ) ) >. ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		ranrcl2.l	Could not format ( ph -> L ( F ( <. C , D >. Ran E ) X ) A ) : No typesetting found for |- ( ph -> L ( F ( <. C , D >. Ran E ) X ) A ) with typecode |-
2	1	ranrcl2	$$⊢\phi \to F\in \left(C\mathrm{Func}D\right)$$
3		opex	$$⊢⟨D,E⟩\in \mathrm{V}$$
4	3	a1i	$$⊢\phi \to ⟨D,E⟩\in \mathrm{V}$$
5	2 4	prcofelvv	Could not format ( ph -> ( <. D , E >. -o.F F ) e. ( _V X. _V ) ) : No typesetting found for |- ( ph -> ( <. D , E >. -o.F F ) e. ( _V X. _V ) ) with typecode |-
6		1st2nd2	Could not format ( ( <. D , E >. -o.F F ) e. ( _V X. _V ) -> ( <. D , E >. -o.F F ) = <. ( 1st ` ( <. D , E >. -o.F F ) ) , ( 2nd ` ( <. D , E >. -o.F F ) ) >. ) : No typesetting found for |- ( ( <. D , E >. -o.F F ) e. ( _V X. _V ) -> ( <. D , E >. -o.F F ) = <. ( 1st ` ( <. D , E >. -o.F F ) ) , ( 2nd ` ( <. D , E >. -o.F F ) ) >. ) with typecode |-
7	5 6	syl	Could not format ( ph -> ( <. D , E >. -o.F F ) = <. ( 1st ` ( <. D , E >. -o.F F ) ) , ( 2nd ` ( <. D , E >. -o.F F ) ) >. ) : No typesetting found for |- ( ph -> ( <. D , E >. -o.F F ) = <. ( 1st ` ( <. D , E >. -o.F F ) ) , ( 2nd ` ( <. D , E >. -o.F F ) ) >. ) with typecode |-