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Mirrors > Home > MPE Home > Th. List > Mathboxes > pwtrrVD | Structured version Visualization version Unicode version |
Description: Virtual deduction proof of pwtr 4921; see pwtrVD 39059 for the converse. (Contributed by Alan Sare, 25-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
pwtrrVD.1 |
Ref | Expression |
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pwtrrVD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dftr2 4754 | . . 3 | |
2 | idn1 38790 | . . . . . . . 8 | |
3 | idn2 38838 | . . . . . . . . 9 | |
4 | simpr 477 | . . . . . . . . 9 | |
5 | 3, 4 | e2 38856 | . . . . . . . 8 |
6 | pwtrrVD.1 | . . . . . . . . 9 | |
7 | 6 | pwid 4174 | . . . . . . . 8 |
8 | trel 4759 | . . . . . . . . 9 | |
9 | 8 | expd 452 | . . . . . . . 8 |
10 | 2, 5, 7, 9 | e120 38888 | . . . . . . 7 |
11 | elpwi 4168 | . . . . . . 7 | |
12 | 10, 11 | e2 38856 | . . . . . 6 |
13 | simpl 473 | . . . . . . 7 | |
14 | 3, 13 | e2 38856 | . . . . . 6 |
15 | ssel 3597 | . . . . . 6 | |
16 | 12, 14, 15 | e22 38896 | . . . . 5 |
17 | 16 | in2 38830 | . . . 4 |
18 | 17 | gen12 38843 | . . 3 |
19 | biimpr 210 | . . 3 | |
20 | 1, 18, 19 | e01 38916 | . 2 |
21 | 20 | in1 38787 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wcel 1990 cvv 3200 wss 3574 cpw 4158 wtr 4752 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-in 3581 df-ss 3588 df-pw 4160 df-uni 4437 df-tr 4753 df-vd1 38786 df-vd2 38794 |
This theorem is referenced by: (None) |
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