syl3an - New Foundations Explorer

	New Foundations Explorer		< Previous Next > Nearby theorems
Mirrors > Home > NFE Home > Th. List > syl3an		Unicode version

Theorem syl3an 1224

Description: A triple syllogism inference. (Contributed by NM, 13-May-2004.)

**Assertion**
Ref	Expression
syl3an	$/\$ $/\$

**Proof of Theorem syl3an**
Step	Hyp	Ref	Expression
1		syl3an.1	. . 3
2		syl3an.2	. . 3
3		syl3an.3	. . 3
4	1, 2, 3	3anim123i 1137	. 2 $/\$ $/\$ $/\$ $/\$
5		syl3an.4	. 2 $/\$ $/\$
6	4, 5	syl 15	1 $/\$ $/\$

Colors of variables: wff setvar class

Syntax hints:

wi 4 $/\$ w3a 934

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8

This theorem depends on definitions: df-bi 177 df-an 360 df-3an 936

This theorem is referenced by: peano5 4409 spfininduct 4540 eloprabga 5578 clos1induct 5880