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Mirrors > Home > MPE Home > Th. List > canth2g | Structured version Unicode version |
Description: Cantor's theorem with the sethood requirement expressed as an antecedent. Theorem 23 of [Suppes] p. 97. (Contributed by NM, 7-Nov-2003.) |
Ref | Expression |
---|---|
canth2g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pweq 3963 |
. . 3
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2 | breq12 4397 |
. . 3
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3 | 1, 2 | mpdan 668 |
. 2
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4 | vex 3073 |
. . 3
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5 | 4 | canth2 7566 |
. 2
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6 | 3, 5 | vtoclg 3128 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-sep 4513 ax-nul 4521 ax-pow 4570 ax-pr 4631 ax-un 6474 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3072 df-sbc 3287 df-csb 3389 df-dif 3431 df-un 3433 df-in 3435 df-ss 3442 df-nul 3738 df-if 3892 df-pw 3962 df-sn 3978 df-pr 3980 df-op 3984 df-uni 4192 df-br 4393 df-opab 4451 df-mpt 4452 df-id 4736 df-xp 4946 df-rel 4947 df-cnv 4948 df-co 4949 df-dm 4950 df-rn 4951 df-res 4952 df-ima 4953 df-iota 5481 df-fun 5520 df-fn 5521 df-f 5522 df-f1 5523 df-fo 5524 df-f1o 5525 df-fv 5526 df-en 7413 df-dom 7414 df-sdom 7415 |
This theorem is referenced by: 2pwuninel 7568 2pwne 7569 pwfi 7709 cdalepw 8468 isfin32i 8637 fin34 8662 hsmexlem1 8698 canth3 8828 ondomon 8830 gchdomtri 8899 canthp1lem1 8922 canthp1lem2 8923 pwfseqlem5 8933 gchcdaidm 8938 gchxpidm 8939 gchpwdom 8940 gchaclem 8948 gchhar 8949 tsksdom 9026 |
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