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Mathbox for Andrew Salmon |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > iotavalb | Structured version Visualization version Unicode version |
Description: Theorem *14.202 in [WhiteheadRussell] p. 189. A biconditional version of iotaval 5580. (Contributed by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
iotavalb |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iotaval 5580 |
. 2
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2 | iotasbc 36815 |
. . . 4
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3 | iotaexeu 36814 |
. . . . 5
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4 | eqsbc3 3319 |
. . . . 5
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5 | 3, 4 | syl 17 |
. . . 4
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6 | 2, 5 | bitr3d 263 |
. . 3
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7 | equequ2 1879 |
. . . . . . 7
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8 | 7 | bibi2d 324 |
. . . . . 6
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9 | 8 | albidv 1778 |
. . . . 5
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10 | 9 | biimpac 493 |
. . . 4
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11 | 10 | exlimiv 1787 |
. . 3
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12 | 6, 11 | syl6bir 237 |
. 2
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13 | 1, 12 | impbid2 209 |
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-or 376 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-rex 2755 df-v 3059 df-sbc 3280 df-un 3421 df-sn 3981 df-pr 3983 df-uni 4213 df-iota 5569 |
This theorem is referenced by: iotavalsb 36829 |
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