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Mirrors > Home > MPE Home > Th. List > reusv2lem1 | Structured version Visualization version Unicode version |
Description: Lemma for reusv2 4609. (Contributed by NM, 22-Oct-2010.) (Proof shortened by Mario Carneiro, 19-Nov-2016.) |
Ref | Expression |
---|---|
reusv2lem1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | n0 3741 |
. . 3
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2 | nfra1 2769 |
. . . . 5
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3 | 2 | nfmo 2316 |
. . . 4
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4 | rsp 2754 |
. . . . . . 7
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5 | 4 | com12 32 |
. . . . . 6
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6 | 5 | alrimiv 1773 |
. . . . 5
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7 | moeq 3214 |
. . . . 5
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8 | moim 2348 |
. . . . 5
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9 | 6, 7, 8 | mpisyl 21 |
. . . 4
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10 | 3, 9 | exlimi 1995 |
. . 3
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11 | 1, 10 | sylbi 199 |
. 2
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12 | eu5 2325 |
. . 3
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13 | 12 | rbaib 917 |
. 2
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14 | 11, 13 | syl 17 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-v 3047 df-dif 3407 df-nul 3732 |
This theorem is referenced by: (None) |
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