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Mirrors > Home > MPE Home > Th. List > 2sb5rf | Structured version Visualization version Unicode version |
Description: Reversed double substitution. (Contributed by NM, 3-Feb-2005.) (Revised by Mario Carneiro, 6-Oct-2016.) Remove distinct variable constraints. (Revised by Wolf Lammen, 28-Sep-2018.) |
Ref | Expression |
---|---|
2sb5rf.1 | |
2sb5rf.2 |
Ref | Expression |
---|---|
2sb5rf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2sb5rf.2 | . . . . 5 | |
2 | 1 | 19.41 2103 | . . . 4 |
3 | 2 | exbii 1774 | . . 3 |
4 | 2sb5rf.1 | . . . 4 | |
5 | 4 | 19.41 2103 | . . 3 |
6 | 3, 5 | bitri 264 | . 2 |
7 | sbequ12r 2112 | . . . . 5 | |
8 | sbequ12r 2112 | . . . . 5 | |
9 | 7, 8 | sylan9bb 736 | . . . 4 |
10 | 9 | pm5.32i 669 | . . 3 |
11 | 10 | 2exbii 1775 | . 2 |
12 | 2ax6e 2450 | . . 3 | |
13 | 12 | biantrur 527 | . 2 |
14 | 6, 11, 13 | 3bitr4ri 293 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wex 1704 wnf 1708 wsb 1880 |
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-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 |
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 |
This theorem is referenced by: sbel2x 2459 |
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