Theorem bj-gabeqd

Description: Equality of generalized class abstractions. Deduction form. (Contributed by BJ, 4-Oct-2024)

	Ref	Expression
Hypotheses	bj-gabeqd.nf	$$⊢\phi \to \forall x\phi$$
	bj-gabeqd.c	$$⊢\phi \to A=B$$
	bj-gabeqd.f	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	bj-gabeqd	Could not format assertion : No typesetting found for |- ( ph -> {{ A | x | ps }} = {{ B | x | ch }} ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		bj-gabeqd.nf	$$⊢\phi \to \forall x\phi$$
2		bj-gabeqd.c	$$⊢\phi \to A=B$$
3		bj-gabeqd.f	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
4	3	biimpd	$$⊢\phi \to \left(\psi \to \chi \right)$$
5	1 2 4	bj-gabssd	Could not format ( ph -> {{ A | x | ps }} C_ {{ B | x | ch }} ) : No typesetting found for |- ( ph -> {{ A | x | ps }} C_ {{ B | x | ch }} ) with typecode |-
6	2	eqcomd	$$⊢\phi \to B=A$$
7	3	biimprd	$$⊢\phi \to \left(\chi \to \psi \right)$$
8	1 6 7	bj-gabssd	Could not format ( ph -> {{ B | x | ch }} C_ {{ A | x | ps }} ) : No typesetting found for |- ( ph -> {{ B | x | ch }} C_ {{ A | x | ps }} ) with typecode |-
9	5 8	eqssd	Could not format ( ph -> {{ A | x | ps }} = {{ B | x | ch }} ) : No typesetting found for |- ( ph -> {{ A | x | ps }} = {{ B | x | ch }} ) with typecode |-