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Mathbox for Alan Sare |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > trsspwALT2 | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of trsspwALT 37269. This proof is the same as the proof of trsspwALT 37269 except each virtual deduction symbol is replaced by its non-virtual deduction symbol equivalent. A transitive class is a subset of its power class. (Contributed by Alan Sare, 23-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
trsspwALT2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 3407 |
. . 3
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2 | id 22 |
. . . . . . 7
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3 | idd 24 |
. . . . . . 7
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4 | trss 4499 |
. . . . . . 7
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5 | 2, 3, 4 | sylsyld 57 |
. . . . . 6
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6 | vex 3034 |
. . . . . . 7
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7 | 6 | elpw 3948 |
. . . . . 6
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8 | 5, 7 | syl6ibr 235 |
. . . . 5
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9 | 8 | idiALT 36902 |
. . . 4
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10 | 9 | alrimiv 1781 |
. . 3
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11 | biimpr 203 |
. . 3
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12 | 1, 10, 11 | mpsyl 64 |
. 2
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13 | 12 | idiALT 36902 |
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-ral 2761 df-v 3033 df-in 3397 df-ss 3404 df-pw 3944 df-uni 4191 df-tr 4491 |
This theorem is referenced by: (None) |
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