kd - brismu bridi

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Theorem kd 24

Description: Deductive form of ax-k 11 Theorem a1d in [ILE] p. 0. (Contributed by la korvo, 30-Jul-2023.)

**Hypothesis**
Ref	Expression
kd.0	⊢ ganai broda gi brode

**Assertion**
Ref	Expression
kd	⊢ ganai broda gi ganai brodi gi brode

**Proof of Theorem kd**
Step	Hyp	Ref	Expression
1		kd.0	. 2 ⊢ ganai broda gi brode
2		ax-k 11	. 2 ⊢ ganai brode gi ganai brodi gi brode
3	1, 2	syl 18	1 ⊢ ganai broda gi ganai brodi gi brode

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 14

This theorem is referenced by: syl5com 25 ge-ganai 42 isod-lem 61