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Theorem bnj561 30947
Description: Technical lemma for bnj852 30965. 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 30944 . 2 (𝜂𝜎)
4 bnj561.37 . 2 ((𝑅 FrSe 𝐴𝜏𝜎) → 𝐺 Fn 𝑛)
53, 4syl3an3 1359 1 ((𝑅 FrSe 𝐴𝜏𝜂) → 𝐺 Fn 𝑛)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  w3a 1036   = wceq 1481  wcel 1988  suc csuc 5713   Fn wfn 5871  ωcom 7050  w-bnj17 30726   FrSe w-bnj15 30732
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-v 3197  df-un 3572  df-sn 4169  df-suc 5717  df-bnj17 30727
This theorem is referenced by:  bnj600  30963  bnj908  30975
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