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Mirrors > Home > MPE Home > Th. List > zfreg | Structured version Visualization version Unicode version |
Description: The Axiom of Regularity
using abbreviations. Axiom 6 of [TakeutiZaring]
p. 21. This is called the "weak form." There is also a
"strong form,"
not requiring that ![]() |
Ref | Expression |
---|---|
zfreg.1 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
zfreg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zfreg.1 |
. . 3
![]() ![]() ![]() ![]() | |
2 | 1 | zfregcl 8114 |
. 2
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3 | n0 3743 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | disj 3807 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | rexbii 2891 |
. 2
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6 | 2, 3, 5 | 3imtr4i 270 |
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-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 ax-reg 8112 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ne 2626 df-ral 2744 df-rex 2745 df-v 3049 df-dif 3409 df-in 3413 df-nul 3734 |
This theorem is referenced by: en3lp 8126 inf3lem3 8140 setindtr 35891 |
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