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Mirrors > Home > MPE Home > Th. List > nfeqf | Structured version Visualization version Unicode version |
Description: A variable is effectively
not free in an equality if it is not either of
the involved variables. ![]() |
Ref | Expression |
---|---|
nfeqf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfna1 1987 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | nfna1 1987 |
. . 3
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3 | 1, 2 | nfan 2013 |
. 2
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4 | equviniv 1874 |
. . 3
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5 | dveeq1 2140 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 5 | imp 431 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | dveeq1 2140 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 7 | imp 431 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | equtr2 1871 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 9 | alanimi 1690 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | 6, 8, 10 | syl2an 480 |
. . . . . 6
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12 | 11 | an4s 836 |
. . . . 5
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13 | 12 | ex 436 |
. . . 4
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14 | 13 | exlimdv 1781 |
. . 3
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15 | 4, 14 | syl5 33 |
. 2
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16 | 3, 15 | nfd 1958 |
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 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-10 1917 ax-12 1935 ax-13 2093 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1666 df-nf 1670 |
This theorem is referenced by: axc9 2142 dvelimf 2170 equveli 2182 2ax6elem 2280 wl-exeq 31879 wl-nfeqfb 31882 wl-equsb4 31897 wl-2sb6d 31900 wl-sbalnae 31904 |
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