brismu bridi		< Previous   Next > Nearby theorems
Mirrors  >  Home  >   Home  >  Th. List  >  ge-ganai

---

Theorem ge-ganai 51

Description: Conjunction implies implication. (Contributed by la korvo, 22-Jun-2024.)

Assertion

Ref	Expression
ge-ganai	⊢ ganai ge broda gi brode gi ganai broda gi brode

---

Proof of Theorem ge-ganai

Step	Hyp	Ref	Expression
1		ax-ge-re 44	. 2 ⊢ ganai ge broda gi brode gi brode
2	1	kd 26	1 ⊢ ganai ge broda gi brode gi ganai broda gi brode

Colors of variables: sumti selbri bridi

Syntax hints:  ge bge 42

This theorem was proved from axioms:  ax-mp 10  ax-k 11  ax-s 15  ax-ge-re 44

This theorem is referenced by:  ge-go  121  subeq-lem1  392

Copyright terms: Public domain

W3C validator