Theorem bnj591

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
Hypothesis	bnj591.1	No typesetting found for |- ( th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode |-
Assertion	bnj591	Could not format assertion : No typesetting found for |- ( [. k / j ]. th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		bnj591.1	Could not format ( th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for |- ( th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode |-
2	1	sbcbii	Could not format ( [. k / j ]. th <-> [. k / j ]. ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) : No typesetting found for |- ( [. k / j ]. th <-> [. k / j ]. ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) ) with typecode |-
3		vex	$$⊢k\in \mathrm{V}$$
4		fveq2	$$⊢j=k\to f\left(j\right)=f\left(k\right)$$
5		fveq2	$$⊢j=k\to g\left(j\right)=g\left(k\right)$$
6	4 5	eqeq12d	$$⊢j=k\to \left(f\left(j\right)=g\left(j\right)\leftrightarrow f\left(k\right)=g\left(k\right)\right)$$
7	6	imbi2d	Could not format ( j = k -> ( ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) ) : No typesetting found for |- ( j = k -> ( ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) ) with typecode |-
8	3 7	sbcie	Could not format ( [. k / j ]. ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) : No typesetting found for |- ( [. k / j ]. ( ( n e. D /\ ch /\ ch' ) -> ( f ` j ) = ( g ` j ) ) <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) with typecode |-
9	2 8	bitri	Could not format ( [. k / j ]. th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) : No typesetting found for |- ( [. k / j ]. th <-> ( ( n e. D /\ ch /\ ch' ) -> ( f ` k ) = ( g ` k ) ) ) with typecode |-