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Mirrors > Home > ILE Home > Th. List > sbimi | Unicode version |
Description: Infer substitution into antecedent and consequent of an implication. (Contributed by NM, 25-Jun-1998.) |
Ref | Expression |
---|---|
sbimi.1 |
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Ref | Expression |
---|---|
sbimi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbimi.1 |
. . . 4
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2 | 1 | imim2i 12 |
. . 3
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3 | 1 | anim2i 340 |
. . . 4
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4 | 3 | eximi 1580 |
. . 3
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5 | 2, 4 | anim12i 336 |
. 2
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6 | df-sb 1737 |
. 2
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7 | df-sb 1737 |
. 2
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8 | 5, 6, 7 | 3imtr4i 200 |
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 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 df-sb 1737 |
This theorem is referenced by: sbbii 1739 sb6f 1776 hbsb3 1781 sbidm 1824 sbco 1942 sbcocom 1944 elsb3 1952 elsb4 1953 sbalyz 1975 hbsb4t 1989 moimv 2066 oprcl 3737 peano1 4516 peano2 4517 |
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