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Theorem bnj562 32203
 Description: Technical lemma for bnj852 32220. 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
bnj562.18 (𝜎 ↔ (𝑚𝐷𝑛 = suc 𝑚𝑝𝑚))
bnj562.19 (𝜂 ↔ (𝑚𝐷𝑛 = suc 𝑚𝑝 ∈ ω ∧ 𝑚 = suc 𝑝))
bnj562.38 ((𝑅 FrSe 𝐴𝜏𝜎) → 𝜑″)
Assertion
Ref Expression
bnj562 ((𝑅 FrSe 𝐴𝜏𝜂) → 𝜑″)

Proof of Theorem bnj562
StepHypRef Expression
1 bnj562.18 . . 3 (𝜎 ↔ (𝑚𝐷𝑛 = suc 𝑚𝑝𝑚))
2 bnj562.19 . . 3 (𝜂 ↔ (𝑚𝐷𝑛 = suc 𝑚𝑝 ∈ ω ∧ 𝑚 = suc 𝑝))
31, 2bnj556 32199 . 2 (𝜂𝜎)
4 bnj562.38 . 2 ((𝑅 FrSe 𝐴𝜏𝜎) → 𝜑″)
53, 4syl3an3 1162 1 ((𝑅 FrSe 𝐴𝜏𝜂) → 𝜑″)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209   ∧ w3a 1084   = wceq 1538   ∈ wcel 2115  suc csuc 6181  ωcom 7571   ∧ w-bnj17 31983   FrSe w-bnj15 31989 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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-un 3924  df-sn 4551  df-suc 6185  df-bnj17 31984 This theorem is referenced by:  bnj600  32218  bnj908  32230
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