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Mathbox for Alan Sare |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > sspwtrALT | Structured version Unicode version |
Description: Virtual deduction proof of sspwtr 31857. This proof is the same as the proof of sspwtr 31857 except each virtual deduction symbol is replaced by its non-virtual deduction symbol equivalent. A class which is a subclass of its power class is transitive. (Contributed by Alan Sare, 3-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
sspwtrALT |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dftr2 4487 |
. . 3
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2 | simpr 461 |
. . . . . 6
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3 | ssel 3450 |
. . . . . 6
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4 | elpwi 3969 |
. . . . . 6
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5 | 2, 3, 4 | syl56 34 |
. . . . 5
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6 | idd 24 |
. . . . . 6
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7 | simpl 457 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 6, 7 | syl6 33 |
. . . . 5
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9 | ssel 3450 |
. . . . 5
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10 | 5, 8, 9 | syl6c 64 |
. . . 4
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11 | 10 | alrimivv 1687 |
. . 3
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12 | bi2 198 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | 1, 11, 12 | mpsyl 63 |
. 2
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14 | 13 | idiALT 31455 |
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 1952 ax-ext 2430 |
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 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-v 3072 df-in 3435 df-ss 3442 df-pw 3962 df-uni 4192 df-tr 4486 |
This theorem is referenced by: (None) |
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