Theorem bj-imdirval

Description: Value of the functionalized direct image. (Contributed by BJ, 16-Dec-2023)

	Ref	Expression
Hypotheses	bj-imdirval.1	$$⊢\phi \to A\in U$$
	bj-imdirval.2	$$⊢\phi \to B\in V$$
Assertion	bj-imdirval	Could not format assertion : No typesetting found for |- ( ph -> ( A ~P_* B ) = ( r e. ~P ( A X. B ) |-> { <. x , y >. | ( ( x C_ A /\ y C_ B ) /\ ( r " x ) = y ) } ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		bj-imdirval.1	$$⊢\phi \to A\in U$$
2		bj-imdirval.2	$$⊢\phi \to B\in V$$
3		df-imdir	Could not format ~P_* = ( a e. _V , b e. _V |-> ( r e. ~P ( a X. b ) |-> { <. x , y >. | ( ( x C_ a /\ y C_ b ) /\ ( r " x ) = y ) } ) ) : No typesetting found for |- ~P_* = ( a e. _V , b e. _V |-> ( r e. ~P ( a X. b ) |-> { <. x , y >. | ( ( x C_ a /\ y C_ b ) /\ ( r " x ) = y ) } ) ) with typecode |-
4	1 2 3	bj-imdirvallem	Could not format ( ph -> ( A ~P_* B ) = ( r e. ~P ( A X. B ) |-> { <. x , y >. | ( ( x C_ A /\ y C_ B ) /\ ( r " x ) = y ) } ) ) : No typesetting found for |- ( ph -> ( A ~P_* B ) = ( r e. ~P ( A X. B ) |-> { <. x , y >. | ( ( x C_ A /\ y C_ B ) /\ ( r " x ) = y ) } ) ) with typecode |-