Theorem bnj1047

Description: Technical lemma for bnj69 . 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
Hypotheses	bnj1047.1	|- ( rh <-> A. j e. n ( j _E i -> [. j / i ]. et ) )
	bnj1047.2	|- ( et' <-> [. j / i ]. et )
Assertion	bnj1047	|- ( rh <-> A. j e. n ( j _E i -> et' ) )

Proof

Step	Hyp	Ref	Expression
1		bnj1047.1	|- ( rh <-> A. j e. n ( j _E i -> [. j / i ]. et ) )
2		bnj1047.2	|- ( et' <-> [. j / i ]. et )
3	2	imbi2i	|- ( ( j _E i -> et' ) <-> ( j _E i -> [. j / i ]. et ) )
4	3	ralbii	|- ( A. j e. n ( j _E i -> et' ) <-> A. j e. n ( j _E i -> [. j / i ]. et ) )
5	1 4	bitr4i	|- ( rh <-> A. j e. n ( j _E i -> et' ) )