Theorem bnj523

Description: Technical lemma for bnj852 . This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj523.1	$$⊢\phi \leftrightarrow F\left(\varnothing \right)=pred\left(X,A,R\right)$$
	bnj523.2	No typesetting found for |- ( ph' <-> [. M / n ]. ph ) with typecode |-
	bnj523.3	$$⊢M\in \mathrm{V}$$
Assertion	bnj523	Could not format assertion : No typesetting found for |- ( ph' <-> ( F ` (/) ) = _pred ( X , A , R ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		bnj523.1	$$⊢\phi \leftrightarrow F\left(\varnothing \right)=pred\left(X,A,R\right)$$
2		bnj523.2	Could not format ( ph' <-> [. M / n ]. ph ) : No typesetting found for |- ( ph' <-> [. M / n ]. ph ) with typecode |-
3		bnj523.3	$$⊢M\in \mathrm{V}$$
4	1	sbcbii	$$⊢\underset{\dot{}}{[}M/n\underset{\dot{}}{]}\phi \leftrightarrow \underset{\dot{}}{[}M/n\underset{\dot{}}{]}F\left(\varnothing \right)=pred\left(X,A,R\right)$$
5	3	bnj525	$$⊢\underset{\dot{}}{[}M/n\underset{\dot{}}{]}F\left(\varnothing \right)=pred\left(X,A,R\right)\leftrightarrow F\left(\varnothing \right)=pred\left(X,A,R\right)$$
6	2 4 5	3bitri	Could not format ( ph' <-> ( F ` (/) ) = _pred ( X , A , R ) ) : No typesetting found for |- ( ph' <-> ( F ` (/) ) = _pred ( X , A , R ) ) with typecode |-