Metamath Proof Explorer


Theorem bnj222

Description: Technical lemma for bnj229 . 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
Hypothesis bnj222.1 ψ i ω suc i N F suc i = y F i pred y A R
Assertion bnj222 ψ m ω suc m N F suc m = y F m pred y A R

Proof

Step Hyp Ref Expression
1 bnj222.1 ψ i ω suc i N F suc i = y F i pred y A R
2 suceq i = m suc i = suc m
3 2 eleq1d i = m suc i N suc m N
4 2 fveq2d i = m F suc i = F suc m
5 fveq2 i = m F i = F m
6 5 bnj1113 i = m y F i pred y A R = y F m pred y A R
7 4 6 eqeq12d i = m F suc i = y F i pred y A R F suc m = y F m pred y A R
8 3 7 imbi12d i = m suc i N F suc i = y F i pred y A R suc m N F suc m = y F m pred y A R
9 8 cbvralvw i ω suc i N F suc i = y F i pred y A R m ω suc m N F suc m = y F m pred y A R
10 1 9 bitri ψ m ω suc m N F suc m = y F m pred y A R