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Mirrors > Home > MPE Home > Th. List > Mathboxes > uun2221p1 | Structured version Visualization version Unicode version |
Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
uun2221p1.1 |
Ref | Expression |
---|---|
uun2221p1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uun2221p1.1 | . . 3 | |
2 | 3anrot 1043 | . . . 4 | |
3 | 2 | imbi1i 339 | . . 3 |
4 | 1, 3 | mpbir 221 | . 2 |
5 | 3anass 1042 | . . . . . 6 | |
6 | anabs5 851 | . . . . . 6 | |
7 | 5, 6 | bitri 264 | . . . . 5 |
8 | ancom 466 | . . . . . 6 | |
9 | 8 | anbi2i 730 | . . . . 5 |
10 | 7, 9 | bitr4i 267 | . . . 4 |
11 | anabs5 851 | . . . . 5 | |
12 | 11, 8 | bitri 264 | . . . 4 |
13 | 10, 12 | bitri 264 | . . 3 |
14 | 13 | imbi1i 339 | . 2 |
15 | 4, 14 | mpbi 220 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-an 386 df-3an 1039 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |