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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > iscsgrpALT | Structured version Visualization version Unicode version |
Description: The predicate "is a commutative semigroup." (Contributed by AV, 20-Jan-2020.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
ismgmALT.b |
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ismgmALT.o |
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Ref | Expression |
---|---|
iscsgrpALT |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq2 5865 |
. . . 4
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2 | fveq2 5865 |
. . . 4
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3 | 1, 2 | breq12d 4415 |
. . 3
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4 | ismgmALT.o |
. . . 4
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5 | ismgmALT.b |
. . . 4
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6 | 4, 5 | breq12i 4411 |
. . 3
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7 | 3, 6 | syl6bbr 267 |
. 2
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8 | df-csgrp2 39911 |
. 2
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9 | 7, 8 | elrab2 3198 |
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-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
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-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 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-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-br 4403 df-iota 5546 df-fv 5590 df-csgrp2 39911 |
This theorem is referenced by: (None) |
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