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Mirrors > Home > ILE Home > Th. List > zfpair2 | Unicode version |
Description: Derive the abbreviated version of the Axiom of Pairing from ax-pr 3935. (Contributed by NM, 14-Nov-2006.) |
Ref | Expression |
---|---|
zfpair2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-pr 3935 |
. . . 4
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2 | 1 | bm1.3ii 3869 |
. . 3
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3 | dfcleq 2031 |
. . . . 5
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4 | vex 2554 |
. . . . . . . 8
![]() ![]() ![]() ![]() | |
5 | 4 | elpr 3385 |
. . . . . . 7
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6 | 5 | bibi2i 216 |
. . . . . 6
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7 | 6 | albii 1356 |
. . . . 5
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8 | 3, 7 | bitri 173 |
. . . 4
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9 | 8 | exbii 1493 |
. . 3
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10 | 2, 9 | mpbir 134 |
. 2
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11 | 10 | issetri 2558 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-pr 3935 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-v 2553 df-un 2916 df-sn 3373 df-pr 3374 |
This theorem is referenced by: prexgOLD 3937 prexg 3938 funopg 4877 |
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