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Theorem bnj561 32297
 Description: Technical lemma for bnj852 32315. 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
bnj561.18 (𝜎 ↔ (𝑚𝐷𝑛 = suc 𝑚𝑝𝑚))
bnj561.19 (𝜂 ↔ (𝑚𝐷𝑛 = suc 𝑚𝑝 ∈ ω ∧ 𝑚 = suc 𝑝))
bnj561.37 ((𝑅 FrSe 𝐴𝜏𝜎) → 𝐺 Fn 𝑛)
Assertion
Ref Expression
bnj561 ((𝑅 FrSe 𝐴𝜏𝜂) → 𝐺 Fn 𝑛)

Proof of Theorem bnj561
StepHypRef Expression
1 bnj561.18 . . 3 (𝜎 ↔ (𝑚𝐷𝑛 = suc 𝑚𝑝𝑚))
2 bnj561.19 . . 3 (𝜂 ↔ (𝑚𝐷𝑛 = suc 𝑚𝑝 ∈ ω ∧ 𝑚 = suc 𝑝))
31, 2bnj556 32294 . 2 (𝜂𝜎)
4 bnj561.37 . 2 ((𝑅 FrSe 𝐴𝜏𝜎) → 𝐺 Fn 𝑛)
53, 4syl3an3 1162 1 ((𝑅 FrSe 𝐴𝜏𝜂) → 𝐺 Fn 𝑛)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209   ∧ w3a 1084   = wceq 1538   ∈ wcel 2111  suc csuc 6161   Fn wfn 6319  ωcom 7562   ∧ w-bnj17 32078   FrSe w-bnj15 32084 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-un 3886  df-sn 4526  df-suc 6165  df-bnj17 32079 This theorem is referenced by:  bnj600  32313  bnj908  32325
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