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Mirrors > Home > ILE Home > Th. List > mpd3an23 | Unicode version |
Description: An inference based on modus ponens. (Contributed by NM, 4-Dec-2006.) |
Ref | Expression |
---|---|
mpd3an23.1 |
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mpd3an23.2 |
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mpd3an23.3 |
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Ref | Expression |
---|---|
mpd3an23 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 |
. 2
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2 | mpd3an23.1 |
. 2
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3 | mpd3an23.2 |
. 2
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4 | mpd3an23.3 |
. 2
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5 | 1, 2, 3, 4 | syl3anc 1238 |
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 |
This theorem depends on definitions: df-bi 117 df-3an 980 |
This theorem is referenced by: exp0 10521 bcpasc 10741 bccl 10742 pw2dvds 12160 qnumdencoprm 12187 qeqnumdivden 12188 grpinvid 12884 mgpvalg 13086 mgpex 13088 opprex 13198 unitgrpid 13240 dvef 14081 |
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