nsyl - brismu bridi

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Theorem nsyl 295

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.1	⊢ ganai broda gi naku brode
nsyl.2	⊢ ganai brodi gi brode

**Assertion**
Ref	Expression
nsyl	⊢ ganai broda gi naku brodi

**Proof of Theorem nsyl**
Step	Hyp	Ref	Expression
1		nsyl.1	. . 3 ⊢ ganai broda gi naku brode
2		nsyl.2	. . 3 ⊢ ganai brodi gi brode
3	1, 2	nsyl3 291	. 2 ⊢ ganai brodi gi naku broda
4	3	con2i 292	1 ⊢ ganai 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 281 ax-efq 284

This theorem is referenced by: stewart 296