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Mathbox for Richard Penner |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege55lem1c | Structured version Visualization version Unicode version |
Description: Necessary deduction regarding substitution of value in equality. (Contributed by RP, 24-Dec-2019.) |
Ref | Expression |
---|---|
frege55lem1c |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sbc 3280 |
. . 3
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2 | eqeq1 2466 |
. . . . 5
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3 | 2 | elabg 3198 |
. . . 4
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4 | 3 | ibi 249 |
. . 3
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5 | 1, 4 | sylbi 200 |
. 2
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6 | 5 | imim2i 16 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-v 3059 df-sbc 3280 |
This theorem is referenced by: frege56c 36560 |
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