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Mirrors > Home > MPE Home > Th. List > resabs2 | Structured version Visualization version Unicode version |
Description: Absorption law for restriction. (Contributed by NM, 27-Mar-1998.) |
Ref | Expression |
---|---|
resabs2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rescom 5132 |
. 2
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2 | resabs1 5136 |
. 2
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3 | 1, 2 | syl5eq 2499 |
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-9 1898 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 ax-sep 4528 ax-nul 4537 ax-pr 4642 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 988 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-rab 2748 df-v 3049 df-dif 3409 df-un 3411 df-in 3413 df-ss 3420 df-nul 3734 df-if 3884 df-sn 3971 df-pr 3973 df-op 3977 df-opab 4465 df-xp 4843 df-rel 4844 df-res 4849 |
This theorem is referenced by: residm 5139 fresaunres2 5760 fourierdlem104 38084 fouriersw 38105 |
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