ganai-comp-lrd - brismu bridi

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Theorem ganai-comp-lrd 45

Description: Deductive form of left-to-right composition. (Contributed by la korvo, 15-Jul-2025.)

**Hypothesis**
Ref	Expression
ganai-comp-lrd.0	⊢ ganai broda gi ganai brode gi brodi

**Assertion**
Ref	Expression
ganai-comp-lrd	⊢ ganai broda gi ganai ganai brodi gi brodo gi ganai brode gi brodo

**Proof of Theorem ganai-comp-lrd**
Step	Hyp	Ref	Expression
1		ganai-comp-lrd.0	. 2 ⊢ ganai broda gi ganai brode gi brodi
2		idd 20	. 2 ⊢ ganai broda gi ganai brodo gi brodo
3	1, 2	imim12d 44	1 ⊢ ganai broda gi ganai ganai brodi gi brodo gi ganai brode gi brodo

Colors of variables: sumti selbri bridi

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

This theorem is referenced by: ganai-comp-lr 46