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Mirrors > Home > MPE Home > Th. List > nfreud | Structured version Visualization version Unicode version |
Description: Deduction version of nfreu 2964. (Contributed by NM, 15-Feb-2013.) (Revised by Mario Carneiro, 8-Oct-2016.) |
Ref | Expression |
---|---|
nfreud.1 |
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nfreud.2 |
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nfreud.3 |
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Ref | Expression |
---|---|
nfreud |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-reu 2743 |
. 2
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2 | nfreud.1 |
. . 3
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3 | nfcvf 2614 |
. . . . . 6
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4 | 3 | adantl 468 |
. . . . 5
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5 | nfreud.2 |
. . . . . 6
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6 | 5 | adantr 467 |
. . . . 5
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7 | 4, 6 | nfeld 2599 |
. . . 4
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8 | nfreud.3 |
. . . . 5
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9 | 8 | adantr 467 |
. . . 4
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10 | 7, 9 | nfand 2007 |
. . 3
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11 | 2, 10 | nfeud2 2310 |
. 2
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12 | 1, 11 | nfxfrd 1696 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 |
This theorem depends on definitions: df-bi 189 df-an 373 df-tru 1446 df-ex 1663 df-nf 1667 df-eu 2302 df-cleq 2443 df-clel 2446 df-nfc 2580 df-reu 2743 |
This theorem is referenced by: nfreu 2964 |
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