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Theorem bnj562 32075
Description: Technical lemma for bnj852 32092. 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 32071 . 2 (𝜂𝜎)
4 bnj562.38 . 2 ((𝑅 FrSe 𝐴𝜏𝜎) → 𝜑″)
53, 4syl3an3 1157 1 ((𝑅 FrSe 𝐴𝜏𝜂) → 𝜑″)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 207  w3a 1079   = wceq 1528  wcel 2105  suc csuc 6186  ωcom 7569  w-bnj17 31855   FrSe w-bnj15 31861
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-3an 1081  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-v 3494  df-un 3938  df-sn 4558  df-suc 6190  df-bnj17 31856
This theorem is referenced by:  bnj600  32090  bnj908  32102
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