Theorem bnj206

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj206.1	No typesetting found for |- ( ph' <-> [. M / n ]. ph ) with typecode |-
	bnj206.2	No typesetting found for |- ( ps' <-> [. M / n ]. ps ) with typecode |-
	bnj206.3	No typesetting found for |- ( ch' <-> [. M / n ]. ch ) with typecode |-
	bnj206.4	$$⊢M\in \mathrm{V}$$
Assertion	bnj206	Could not format assertion : No typesetting found for |- ( [. M / n ]. ( ph /\ ps /\ ch ) <-> ( ph' /\ ps' /\ ch' ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		bnj206.1	Could not format ( ph' <-> [. M / n ]. ph ) : No typesetting found for |- ( ph' <-> [. M / n ]. ph ) with typecode |-
2		bnj206.2	Could not format ( ps' <-> [. M / n ]. ps ) : No typesetting found for |- ( ps' <-> [. M / n ]. ps ) with typecode |-
3		bnj206.3	Could not format ( ch' <-> [. M / n ]. ch ) : No typesetting found for |- ( ch' <-> [. M / n ]. ch ) with typecode |-
4		bnj206.4	$$⊢M\in \mathrm{V}$$
5		sbc3an	$$⊢\underset{\dot{}}{[}M/n\underset{\dot{}}{]}\left(\phi \wedge \psi \wedge \chi \right)\leftrightarrow \left(\underset{\dot{}}{[}M/n\underset{\dot{}}{]}\phi \wedge \underset{\dot{}}{[}M/n\underset{\dot{}}{]}\psi \wedge \underset{\dot{}}{[}M/n\underset{\dot{}}{]}\chi \right)$$
6	1	bicomi	Could not format ( [. M / n ]. ph <-> ph' ) : No typesetting found for |- ( [. M / n ]. ph <-> ph' ) with typecode |-
7	2	bicomi	Could not format ( [. M / n ]. ps <-> ps' ) : No typesetting found for |- ( [. M / n ]. ps <-> ps' ) with typecode |-
8	3	bicomi	Could not format ( [. M / n ]. ch <-> ch' ) : No typesetting found for |- ( [. M / n ]. ch <-> ch' ) with typecode |-
9	6 7 8	3anbi123i	Could not format ( ( [. M / n ]. ph /\ [. M / n ]. ps /\ [. M / n ]. ch ) <-> ( ph' /\ ps' /\ ch' ) ) : No typesetting found for |- ( ( [. M / n ]. ph /\ [. M / n ]. ps /\ [. M / n ]. ch ) <-> ( ph' /\ ps' /\ ch' ) ) with typecode |-
10	5 9	bitri	Could not format ( [. M / n ]. ( ph /\ ps /\ ch ) <-> ( ph' /\ ps' /\ ch' ) ) : No typesetting found for |- ( [. M / n ]. ( ph /\ ps /\ ch ) <-> ( ph' /\ ps' /\ ch' ) ) with typecode |-