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Theorem bnj561 34433
Description: Technical lemma for bnj852 34451. 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 34430 . 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 205  w3a 1084   = wceq 1533  wcel 2098  suc csuc 6357   Fn wfn 6529  ωcom 7849  w-bnj17 34216   FrSe w-bnj15 34222
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-un 3946  df-sn 4622  df-suc 6361  df-bnj17 34217
This theorem is referenced by:  bnj600  34449  bnj908  34461
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