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Mirrors > Home > ILE Home > Th. List > mpsyl | Unicode version |
Description: Modus ponens combined with a syllogism inference. (Contributed by Alan Sare, 20-Apr-2011.) |
Ref | Expression |
---|---|
mpsyl.1 |
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mpsyl.2 |
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mpsyl.3 |
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Ref | Expression |
---|---|
mpsyl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpsyl.1 |
. . 3
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2 | 1 | a1i 9 |
. 2
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3 | mpsyl.2 |
. 2
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4 | mpsyl.3 |
. 2
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5 | 2, 3, 4 | sylc 56 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 |
This theorem is referenced by: relcnvtr 4783 relresfld 4790 relcoi1 4792 funco 4883 foimacnv 5087 fvi 5173 isoini2 5401 ovidig 5560 smores2 5850 tfrlem5 5871 cauappcvgprlemm 6617 caucvgprlemm 6639 |
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