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Mirrors > Home > MPE Home > Th. List > axregndlem1 | Structured version Visualization version Unicode version |
Description: Lemma for the Axiom of Regularity with no distinct variable conditions. (Contributed by NM, 3-Jan-2002.) |
Ref | Expression |
---|---|
axregndlem1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.8a 1935 |
. 2
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2 | nfae 2150 |
. . 3
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3 | nfae 2150 |
. . . . . 6
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4 | elirrv 8112 |
. . . . . . . . 9
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5 | elequ1 1894 |
. . . . . . . . 9
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6 | 4, 5 | mtbii 304 |
. . . . . . . 8
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7 | 6 | sps 1943 |
. . . . . . 7
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8 | 7 | pm2.21d 110 |
. . . . . 6
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9 | 3, 8 | alrimi 1955 |
. . . . 5
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10 | 9 | anim2i 573 |
. . . 4
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11 | 10 | expcom 437 |
. . 3
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12 | 2, 11 | eximd 1960 |
. 2
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13 | 1, 12 | syl5 33 |
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-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pr 4639 ax-reg 8107 |
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-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-v 3047 df-dif 3407 df-un 3409 df-nul 3732 df-sn 3969 df-pr 3971 |
This theorem is referenced by: axregndlem2 9028 axregnd 9029 |
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