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Theorem bnj561 32879
Description: Technical lemma for bnj852 32897. 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 32876 . 2 (𝜂𝜎)
4 bnj561.37 . 2 ((𝑅 FrSe 𝐴𝜏𝜎) → 𝐺 Fn 𝑛)
53, 4syl3an3 1164 1 ((𝑅 FrSe 𝐴𝜏𝜂) → 𝐺 Fn 𝑛)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  w3a 1086   = wceq 1542  wcel 2110  suc csuc 6267   Fn wfn 6427  ωcom 7706  w-bnj17 32661   FrSe w-bnj15 32667
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-ext 2711
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1545  df-ex 1787  df-sb 2072  df-clab 2718  df-cleq 2732  df-clel 2818  df-v 3433  df-un 3897  df-sn 4568  df-suc 6271  df-bnj17 32662
This theorem is referenced by:  bnj600  32895  bnj908  32907
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