ge-prod - brismu bridi

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

Theorem ge-prod 69

Description: All binary products exist. (Contributed by la korvo, 22-Jun-2024.)

**Hypotheses**
Ref	Expression
ge-prod.0	⊢ ganai broda gi brode
ge-prod.1	⊢ ganai broda gi brodi

**Assertion**
Ref	Expression
ge-prod	⊢ ganai broda gi ge brode gi brodi

**Proof of Theorem ge-prod**
Step	Hyp	Ref	Expression
1		ge-prod.0	. 2 ⊢ ganai broda gi brode
2		ge-prod.1	. 2 ⊢ ganai broda gi brodi
3		ax-ge-in 50	. 2 ⊢ ganai brode gi ganai brodi gi ge brode gi brodi
4	1, 2, 3	sylc 35	1 ⊢ ganai broda gi ge brode gi brodi

Colors of variables: sumti selbri bridi

Syntax hints: ge bge 47

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

This theorem is referenced by: sylanbrc 107 ga-dist-ge 182 ge-dist-ex 431