Theorem bnj934

Description: Technical lemma for bnj69 . 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	bnj934.1	$$⊢\phi \leftrightarrow f\left(\varnothing \right)=pred\left(X,A,R\right)$$
	bnj934.4	No typesetting found for |- ( ph' <-> [. p / n ]. ph ) with typecode |-
	bnj934.7	No typesetting found for |- ( ph" <-> [. G / f ]. ph' ) with typecode |-
	bnj934.50	$$⊢G\in \mathrm{V}$$
Assertion	bnj934	Could not format assertion : No typesetting found for |- ( ( ph /\ ( G ` (/) ) = ( f ` (/) ) ) -> ph" ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		bnj934.1	$$⊢\phi \leftrightarrow f\left(\varnothing \right)=pred\left(X,A,R\right)$$
2		bnj934.4	Could not format ( ph' <-> [. p / n ]. ph ) : No typesetting found for |- ( ph' <-> [. p / n ]. ph ) with typecode |-
3		bnj934.7	Could not format ( ph" <-> [. G / f ]. ph' ) : No typesetting found for |- ( ph" <-> [. G / f ]. ph' ) with typecode |-
4		bnj934.50	$$⊢G\in \mathrm{V}$$
5		eqtr	$$⊢\left(G\left(\varnothing \right)=f\left(\varnothing \right)\wedge f\left(\varnothing \right)=pred\left(X,A,R\right)\right)\to G\left(\varnothing \right)=pred\left(X,A,R\right)$$
6	1 5	sylan2b	$$⊢\left(G\left(\varnothing \right)=f\left(\varnothing \right)\wedge \phi \right)\to G\left(\varnothing \right)=pred\left(X,A,R\right)$$
7		vex	$$⊢p\in \mathrm{V}$$
8	1 2 7	bnj523	Could not format ( ph' <-> ( f ` (/) ) = _pred ( X , A , R ) ) : No typesetting found for |- ( ph' <-> ( f ` (/) ) = _pred ( X , A , R ) ) with typecode |-
9	8 1	bitr4i	Could not format ( ph' <-> ph ) : No typesetting found for |- ( ph' <-> ph ) with typecode |-
10	9	sbcbii	Could not format ( [. G / f ]. ph' <-> [. G / f ]. ph ) : No typesetting found for |- ( [. G / f ]. ph' <-> [. G / f ]. ph ) with typecode |-
11	3 10	bitri	Could not format ( ph" <-> [. G / f ]. ph ) : No typesetting found for |- ( ph" <-> [. G / f ]. ph ) with typecode |-
12	1 11 4	bnj609	Could not format ( ph" <-> ( G ` (/) ) = _pred ( X , A , R ) ) : No typesetting found for |- ( ph" <-> ( G ` (/) ) = _pred ( X , A , R ) ) with typecode |-
13	6 12	sylibr	Could not format ( ( ( G ` (/) ) = ( f ` (/) ) /\ ph ) -> ph" ) : No typesetting found for |- ( ( ( G ` (/) ) = ( f ` (/) ) /\ ph ) -> ph" ) with typecode |-
14	13	ancoms	Could not format ( ( ph /\ ( G ` (/) ) = ( f ` (/) ) ) -> ph" ) : No typesetting found for |- ( ( ph /\ ( G ` (/) ) = ( f ` (/) ) ) -> ph" ) with typecode |-