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Mirrors > Home > MPE Home > Th. List > Mathboxes > mapdordlem1bN | Structured version Visualization version GIF version |
Description: Lemma for mapdord 41048. (Contributed by NM, 27-Jan-2015.) (New usage is discouraged.) |
Ref | Expression |
---|---|
mapdordlem1b.c | ⊢ 𝐶 = {𝑔 ∈ 𝐹 ∣ (𝑂‘(𝑂‘(𝐿‘𝑔))) = (𝐿‘𝑔)} |
Ref | Expression |
---|---|
mapdordlem1bN | ⊢ (𝐽 ∈ 𝐶 ↔ (𝐽 ∈ 𝐹 ∧ (𝑂‘(𝑂‘(𝐿‘𝐽))) = (𝐿‘𝐽))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mapdordlem1b.c | . 2 ⊢ 𝐶 = {𝑔 ∈ 𝐹 ∣ (𝑂‘(𝑂‘(𝐿‘𝑔))) = (𝐿‘𝑔)} | |
2 | 1 | lcfl1lem 40901 | 1 ⊢ (𝐽 ∈ 𝐶 ↔ (𝐽 ∈ 𝐹 ∧ (𝑂‘(𝑂‘(𝐿‘𝐽))) = (𝐿‘𝐽))) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∧ wa 395 = wceq 1534 ∈ wcel 2099 {crab 3427 ‘cfv 6542 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-ext 2698 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2705 df-cleq 2719 df-clel 2805 df-rab 3428 df-v 3471 df-dif 3947 df-un 3949 df-in 3951 df-ss 3961 df-nul 4319 df-if 4525 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4904 df-br 5143 df-iota 6494 df-fv 6550 |
This theorem is referenced by: (None) |
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