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Theorem bnj562 30228
 Description: Technical lemma for bnj852 30245. 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 30224 . 2 (𝜂𝜎)
4 bnj562.38 . 2 ((𝑅 FrSe 𝐴𝜏𝜎) → 𝜑″)
53, 4syl3an3 1353 1 ((𝑅 FrSe 𝐴𝜏𝜂) → 𝜑″)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195   ∧ w3a 1031   = wceq 1475   ∈ wcel 1977  suc csuc 5642  ωcom 6957   ∧ w-bnj17 30005   FrSe w-bnj15 30011 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-un 3545  df-sn 4126  df-suc 5646  df-bnj17 30006 This theorem is referenced by:  bnj600  30243  bnj908  30255
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