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Mirrors > Home > MPE Home > Th. List > ensymb | Structured version Visualization version Unicode version |
Description: Symmetry of equinumerosity. Theorem 2 of [Suppes] p. 92. (Contributed by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
ensymb |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ener 7616 |
. . . 4
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2 | 1 | a1i 11 |
. . 3
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3 | 2 | ersymb 7377 |
. 2
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4 | 3 | trud 1453 |
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-pow 4581 ax-pr 4639 ax-un 6583 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3047 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-pw 3953 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-br 4403 df-opab 4462 df-id 4749 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-fun 5584 df-fn 5585 df-f 5586 df-f1 5587 df-fo 5588 df-f1o 5589 df-er 7363 df-en 7570 |
This theorem is referenced by: ensym 7618 0sdomg 7701 snnen2o 7761 cantnfp1lem2 8184 cantnflem1 8194 iscard2 8410 dffin1-5 8818 pmtrsn 17160 volmeas 29054 carsgclctunlem3 29152 isnumbasgrplem1 35960 rp-isfinite6 36163 |
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