Theorem bnj1047 31041

Description: Technical lemma for bnj69 31078. 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.)

Hypotheses

Ref	Expression
bnj1047.1	|- ( rh <-> A. j e. n ( j _E i -> [. j / i ]. et ) )
bnj1047.2	|- ( et' <-> [. j / i ]. et )

Assertion

Ref	Expression
bnj1047	|- ( rh <-> A. j e. n ( j _E i -> et' ) )

Proof of Theorem bnj1047

Step	Hyp	Ref	Expression
1		bnj1047.1	. 2 |- ( rh <-> A. j e. n ( j _E i -> [. j / i ]. et ) )
2		bnj1047.2	. . . 4 |- ( et' <-> [. j / i ]. et )
3	2	imbi2i 326	. . 3 |- ( ( j _E i -> et' ) <-> ( j _E i -> [. j / i ]. et ) )
4	3	ralbii 2980	. 2 |- ( A. j e. n ( j _E i -> et' ) <-> A. j e. n ( j _E i -> [. j / i ]. et ) )
5	1, 4	bitr4i 267	1 |- ( rh <-> A. j e. n ( j _E i -> et' ) )

Syntax hints:   -> wi 4   <-> wb 196   A.wral 2912   [.wsbc 3435   class class class wbr 4653   _E cep 5028

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-ral 2917

This theorem is referenced by: (None)