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Theorem bnj562 31100
Description: Technical lemma for bnj852 31117. 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 31096 . 2 (𝜂𝜎)
4 bnj562.38 . 2 ((𝑅 FrSe 𝐴𝜏𝜎) → 𝜑″)
53, 4syl3an3 1401 1 ((𝑅 FrSe 𝐴𝜏𝜂) → 𝜑″)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  w3a 1054   = wceq 1523  wcel 2030  suc csuc 5763  ωcom 7107  w-bnj17 30880   FrSe w-bnj15 30886
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-un 3612  df-sn 4211  df-suc 5767  df-bnj17 30881
This theorem is referenced by:  bnj600  31115  bnj908  31127
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