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	$$⊢\chi \leftrightarrow \left(fFnn\wedge \phi \wedge \psi \right)$$
	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	$$⊢\chi \leftrightarrow \left(fFnn\wedge \phi \wedge \psi \right)$$
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	$$⊢\underset{\dot{}}{[}g/f\underset{\dot{}}{]}\chi \leftrightarrow \underset{\dot{}}{[}g/f\underset{\dot{}}{]}\left(fFnn\wedge \phi \wedge \psi \right)$$
6		sbc3an	$$⊢\underset{\dot{}}{[}g/f\underset{\dot{}}{]}\left(fFnn\wedge \phi \wedge \psi \right)\leftrightarrow \left(\underset{\dot{}}{[}g/f\underset{\dot{}}{]}fFnn\wedge \underset{\dot{}}{[}g/f\underset{\dot{}}{]}\phi \wedge \underset{\dot{}}{[}g/f\underset{\dot{}}{]}\psi \right)$$
7		bnj62	$$⊢\underset{\dot{}}{[}g/f\underset{\dot{}}{]}fFnn\leftrightarrow gFnn$$
8	7	bicomi	$$⊢gFnn\leftrightarrow \underset{\dot{}}{[}g/f\underset{\dot{}}{]}fFnn$$
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 |-