# Metamath Proof Explorer

## Theorem bnj581

Description: Technical lemma for bnj580 . 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) Remove unnecessary distinct variable conditions. (Revised by Andrew Salmon, 9-Jul-2011) (New usage is discouraged.)

Ref Expression
Hypotheses bnj581.3 ${⊢}{\chi }↔\left({f}Fn{n}\wedge {\phi }\wedge {\psi }\right)$
bnj581.4 No typesetting found for |- ( ph' <-> [. g / f ]. ph ) with typecode |-
bnj581.5 No typesetting found for |- ( ps' <-> [. g / f ]. ps ) with typecode |-
bnj581.6 No typesetting found for |- ( ch' <-> [. g / f ]. ch ) with typecode |-
Assertion bnj581 Could not format assertion : No typesetting found for |- ( ch' <-> ( g Fn n /\ ph' /\ ps' ) ) with typecode |-

### Proof

Step Hyp Ref Expression
1 bnj581.3 ${⊢}{\chi }↔\left({f}Fn{n}\wedge {\phi }\wedge {\psi }\right)$
2 bnj581.4 Could not format ( ph' <-> [. g / f ]. ph ) : No typesetting found for |- ( ph' <-> [. g / f ]. ph ) with typecode |-
3 bnj581.5 Could not format ( ps' <-> [. g / f ]. ps ) : No typesetting found for |- ( ps' <-> [. g / f ]. ps ) with typecode |-
4 bnj581.6 Could not format ( ch' <-> [. g / f ]. ch ) : No typesetting found for |- ( ch' <-> [. g / f ]. ch ) with typecode |-
5 1 sbcbii
6 sbc3an
7 bnj62
8 7 bicomi
9 8 2 3 3anbi123i Could not format ( ( g Fn n /\ ph' /\ ps' ) <-> ( [. g / f ]. f Fn n /\ [. g / f ]. ph /\ [. g / f ]. ps ) ) : No typesetting found for |- ( ( g Fn n /\ ph' /\ ps' ) <-> ( [. g / f ]. f Fn n /\ [. g / f ]. ph /\ [. g / f ]. ps ) ) with typecode |-
10 6 9 bitr4i Could not format ( [. g / f ]. ( f Fn n /\ ph /\ ps ) <-> ( g Fn n /\ ph' /\ ps' ) ) : No typesetting found for |- ( [. g / f ]. ( f Fn n /\ ph /\ ps ) <-> ( g Fn n /\ ph' /\ ps' ) ) with typecode |-
11 4 5 10 3bitri Could not format ( ch' <-> ( g Fn n /\ ph' /\ ps' ) ) : No typesetting found for |- ( ch' <-> ( g Fn n /\ ph' /\ ps' ) ) with typecode |-