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Mathbox for Alan Sare |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > sstrALT2 | Structured version Unicode version |
Description: Virtual deduction proof of sstr 3467, transitivity of subclasses, Theorem 6 of [Suppes] p. 23. This theorem was automatically generated from sstrALT2VD 31883 using the command file translatewithout_overwriting.cmd . It was not minimized because the automated minimization excluding duplicates generates a minimized proof which, although not directly containing any duplicates, indirectly contains a duplicate. That is, the trace back of the minimized proof contains a duplicate. This is undesirable because some step(s) of the minimized proof use the proven theorem. (Contributed by Alan Sare, 11-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
sstrALT2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 3448 |
. 2
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2 | id 22 |
. . . . . 6
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3 | simpr 461 |
. . . . . 6
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4 | 2, 3 | syl 16 |
. . . . 5
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5 | simpl 457 |
. . . . . . 7
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6 | 2, 5 | syl 16 |
. . . . . 6
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7 | idd 24 |
. . . . . 6
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8 | ssel2 3454 |
. . . . . 6
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9 | 6, 7, 8 | syl6an 545 |
. . . . 5
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10 | ssel2 3454 |
. . . . 5
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11 | 4, 9, 10 | syl6an 545 |
. . . 4
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12 | 11 | idiALT 31466 |
. . 3
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13 | 12 | alrimiv 1686 |
. 2
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14 | bi2 198 |
. 2
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15 | 1, 13, 14 | mpsyl 63 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1954 ax-ext 2431 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2438 df-cleq 2444 df-clel 2447 df-in 3438 df-ss 3445 |
This theorem is referenced by: (None) |
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