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Mirrors > Home > MPE Home > Th. List > jaao | Unicode version |
Description: Inference conjoining and disjoining the antecedents of two implications. (Contributed by NM, 30-Sep-1999.) |
Ref | Expression |
---|---|
jaao.1 | |
jaao.2 |
Ref | Expression |
---|---|
jaao |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | jaao.1 | . . 3 | |
2 | 1 | adantr 465 | . 2 |
3 | jaao.2 | . . 3 | |
4 | 3 | adantl 466 | . 2 |
5 | 2, 4 | jaod 380 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -> wi 4 \/ wo 368
/\ wa 369 |
This theorem is referenced by: pm3.44 511 pm3.48 833 prlem1 962 ordtri1 4916 ordun 4984 suc11 4986 funun 5635 poxp 6912 suc11reg 8057 rankunb 8289 gruun 9205 ofpreima2 27508 |
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 185 df-or 370 df-an 371 |
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