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Theorem bnj562 33183
Description: Technical lemma for bnj852 33200. 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 33179 . 2 (𝜂𝜎)
4 bnj562.38 . 2 ((𝑅 FrSe 𝐴𝜏𝜎) → 𝜑″)
53, 4syl3an3 1164 1 ((𝑅 FrSe 𝐴𝜏𝜂) → 𝜑″)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  w3a 1086   = wceq 1540  wcel 2105  suc csuc 6305  ωcom 7781  w-bnj17 32965   FrSe w-bnj15 32971
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3443  df-un 3903  df-sn 4575  df-suc 6309  df-bnj17 32966
This theorem is referenced by:  bnj600  33198  bnj908  33210
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