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Mirrors > Home > ILE Home > Th. List > orbi2i | Unicode version |
Description: Inference adding a left disjunct to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Dec-2012.) |
Ref | Expression |
---|---|
orbi2i.1 |
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Ref | Expression |
---|---|
orbi2i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orbi2i.1 |
. . . 4
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2 | 1 | biimpi 120 |
. . 3
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3 | 2 | orim2i 761 |
. 2
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4 | 1 | biimpri 133 |
. . 3
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5 | 4 | orim2i 761 |
. 2
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6 | 3, 5 | impbii 126 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: orbi1i 763 orbi12i 764 orass 767 or4 771 or42 772 orordir 774 dcnnOLD 849 orbididc 953 3orcomb 987 excxor 1378 xordc 1392 nf4dc 1670 nf4r 1671 19.44 1682 dveeq2 1815 dvelimALT 2010 dvelimfv 2011 dvelimor 2018 dcne 2358 unass 3293 undi 3384 undif3ss 3397 symdifxor 3402 undif4 3486 iinuniss 3970 ordsucim 4500 suc11g 4557 qfto 5019 nntri3or 6494 reapcotr 8555 elnn0 9178 elxnn0 9241 elnn1uz2 9607 nn01to3 9617 elxr 9776 xaddcom 9861 xnegdi 9868 xpncan 9871 xleadd1a 9873 lcmdvds 12079 mulgcddvds 12094 cncongr2 12104 pythagtrip 12283 bj-peano4 14710 apdifflemr 14798 |
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