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Mirrors > Home > MPE Home > Th. List > ontrciOLD | Structured version Visualization version GIF version |
Description: Obsolete version of ontr 6467 as of 28-Dec-2024. (Contributed by NM, 11-Jun-1994.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
on.1 | ⊢ 𝐴 ∈ On |
Ref | Expression |
---|---|
ontrciOLD | ⊢ Tr 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | on.1 | . 2 ⊢ 𝐴 ∈ On | |
2 | ontr 6467 | . 2 ⊢ (𝐴 ∈ On → Tr 𝐴) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ Tr 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2098 Tr wtr 5258 Oncon0 6358 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2697 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2704 df-cleq 2718 df-clel 2804 df-ral 3056 df-v 3470 df-in 3950 df-ss 3960 df-uni 4903 df-tr 5259 df-po 5581 df-so 5582 df-fr 5624 df-we 5626 df-ord 6361 df-on 6362 |
This theorem is referenced by: (None) |
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