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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege54cor1c | Structured version Visualization version Unicode version |
Description: Reflexive equality. (Contributed by RP, 24-Dec-2019.) (Revised by RP, 25-Apr-2020.) |
Ref | Expression |
---|---|
frege54c.1 |
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Ref | Expression |
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frege54cor1c |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege54c.1 |
. . . . 5
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2 | 1 | elexi 3041 |
. . . 4
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3 | 2 | snid 3988 |
. . 3
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4 | df-sn 3960 |
. . 3
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5 | 3, 4 | eleqtri 2547 |
. 2
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6 | df-sbc 3256 |
. 2
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7 | 5, 6 | mpbir 214 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-an 378 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-v 3033 df-sbc 3256 df-sn 3960 |
This theorem is referenced by: frege55lem2c 36584 frege55c 36585 frege56c 36586 |
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