Metamath Proof Explorer


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 V
4 fveq2 j = k f j = f k
5 fveq2 j = k g j = g k
6 4 5 eqeq12d j = k f j = g j f k = g k
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 |-