Theorem camestres 2005

Description: "Camestres", one of the syllogisms of Aristotelian logic. All ph is ps, and no ch is ps, therefore no ch is ph. (In Aristotelian notation, AEE-2: PaM and SeM therefore SeP.) (Contributed by David A. Wheeler, 28-Aug-2016.) (Revised by David A. Wheeler, 2-Sep-2016.)

Hypotheses

Ref	Expression
camestres.maj	|- A. x ( ph -> ps )
camestres.min	|- A. x ( ch -> -. ps )

Assertion

Ref	Expression
camestres	|- A. x ( ch -> -. ph )

Proof of Theorem camestres

Step	Hyp	Ref	Expression
1		camestres.min	. . . 4 |- A. x ( ch -> -. ps )
2	1	spi 1429	. . 3 |- ( ch -> -. ps )
3		camestres.maj	. . . 4 |- A. x ( ph -> ps )
4	3	spi 1429	. . 3 |- ( ph -> ps )
5	2, 4	nsyl 558	. 2 |- ( ch -> -. ph )
6	5	ax-gen 1338	1 |- A. x ( ch -> -. ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 544  ax-in2 545  ax-gen 1338  ax-4 1400

This theorem is referenced by: (None)