sylan2 - brismu bridi

	brismu bridi		< Previous Next > Nearby theorems
Mirrors > Home > Home > Th. List > sylan2

Theorem sylan2 68

Description: A syllogism weakening the antecedent. (Contributed by la korvo, 9-Jul-2025.)

**Hypotheses**
Ref	Expression
sylan2.0	⊢ ganai broda gi brodi
sylan2.1	⊢ ganai ge brode gi brodi gi brodo

**Assertion**
Ref	Expression
sylan2	⊢ ganai ge brode gi broda gi brodo

**Proof of Theorem sylan2**
Step	Hyp	Ref	Expression
1		sylan2.0	. . 3 ⊢ ganai broda gi brodi
2	1	weakal 67	. 2 ⊢ ganai ge brode gi broda gi brodi
3		sylan2.1	. 2 ⊢ ganai ge brode gi brodi gi brodo
4	2, 3	syldan 66	1 ⊢ ganai ge brode gi broda gi brodo

Colors of variables: sumti selbri bridi

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-le 48 ax-ge-re 49 ax-ge-in 50

This theorem is referenced by: syl2an 78