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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1071 | Structured version Visualization version GIF version |
Description: Technical lemma for bnj69 32284. 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.) |
Ref | Expression |
---|---|
bnj1071.7 | ⊢ 𝐷 = (ω ∖ {∅}) |
Ref | Expression |
---|---|
bnj1071 | ⊢ (𝑛 ∈ 𝐷 → E Fr 𝑛) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1071.7 | . . 3 ⊢ 𝐷 = (ω ∖ {∅}) | |
2 | 1 | bnj923 32041 | . 2 ⊢ (𝑛 ∈ 𝐷 → 𝑛 ∈ ω) |
3 | nnord 7590 | . 2 ⊢ (𝑛 ∈ ω → Ord 𝑛) | |
4 | ordfr 6208 | . 2 ⊢ (Ord 𝑛 → E Fr 𝑛) | |
5 | 2, 3, 4 | 3syl 18 | 1 ⊢ (𝑛 ∈ 𝐷 → E Fr 𝑛) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1537 ∈ wcel 2114 ∖ cdif 3935 ∅c0 4293 {csn 4569 E cep 5466 Fr wfr 5513 Ord word 6192 ωcom 7582 |
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 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 ax-sep 5205 ax-nul 5212 ax-pr 5332 ax-un 7463 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3or 1084 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-mo 2622 df-eu 2654 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-ne 3019 df-ral 3145 df-rex 3146 df-rab 3149 df-v 3498 df-sbc 3775 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-pss 3956 df-nul 4294 df-if 4470 df-sn 4570 df-pr 4572 df-tp 4574 df-op 4576 df-uni 4841 df-br 5069 df-opab 5131 df-tr 5175 df-eprel 5467 df-po 5476 df-so 5477 df-fr 5516 df-we 5518 df-ord 6196 df-on 6197 df-lim 6198 df-suc 6199 df-om 7583 |
This theorem is referenced by: bnj1030 32261 bnj1133 32263 |
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