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Mirrors > Home > MPE Home > Th. List > bija | Structured version Visualization version Unicode version |
Description: Combine antecedents into a single biconditional. This inference, reminiscent of ja 173, is reversible: The hypotheses can be deduced from the conclusion alone (see pm5.1im 253 and pm5.21im 364). (Contributed by Wolf Lammen, 13-May-2013.) |
Ref | Expression |
---|---|
bija.1 | |
bija.2 |
Ref | Expression |
---|---|
bija |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biimpr 210 | . . 3 | |
2 | bija.1 | . . 3 | |
3 | 1, 2 | syli 39 | . 2 |
4 | biimp 205 | . . . 4 | |
5 | 4 | con3d 148 | . . 3 |
6 | bija.2 | . . 3 | |
7 | 5, 6 | syli 39 | . 2 |
8 | 3, 7 | pm2.61d 170 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 |
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 |
This theorem is referenced by: equvel 2347 2lgsoddprm 25141 bj-bibibi 32571 wl-aleq 33322 wl-nfeqfb 33323 rp-fakeimass 37857 rp-fakenanass 37860 |
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