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Mirrors > Home > ILE Home > Th. List > rexm | Unicode version |
Description: Restricted existential quantification implies its restriction is inhabited. (Contributed by Jim Kingdon, 16-Oct-2018.) |
Ref | Expression |
---|---|
rexm |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2461 |
. 2
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2 | simpl 109 |
. . 3
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3 | 2 | eximi 1600 |
. 2
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4 | 1, 3 | sylbi 121 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-ial 1534 |
This theorem depends on definitions: df-bi 117 df-rex 2461 |
This theorem is referenced by: elrelimasn 4994 eusvobj2 5860 exmidomni 7139 fodjum 7143 ismgmid 12790 ismnd 12814 dfgrp2e 12897 |
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