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Theorem nsyl 258
Description: A negated syllogism. Can be seen as a deduction form of modus tollens. (Contributed by la korvo, 1-Jan-2025.)
Hypotheses
Ref Expression
nsyl.1ganai broda gi naku brode
nsyl.2ganai brodi gi brode
Assertion
Ref Expression
nsylganai broda gi naku brodi

Proof of Theorem nsyl
StepHypRef Expression
1 nsyl.1 . . 3ganai broda gi naku brode
2 nsyl.2 . . 3ganai brodi gi brode
31, 2nsyl3 254 . 2ganai brodi gi naku broda
43con2i 255 1ganai broda gi naku brodi
Colors of variables: sumti selbri bridi
This theorem was proved from axioms:  ax-mp 10  ax-k 11  ax-s 15  ax-sdo 245  ax-efq 248
This theorem is referenced by:  stewart  259
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