imim12d - brismu bridi

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Theorem imim12d 44

Description: A deduction interleaving two implications. (Contributed by la korvo, 15-Jul-2025.)

**Hypotheses**
Ref	Expression
imim12d.0	⊢ ganai broda gi ganai brode gi brodi
imim12d.1	⊢ ganai broda gi ganai brodo gi brodu

**Assertion**
Ref	Expression
imim12d	⊢ ganai broda gi ganai ganai brodi gi brodo gi ganai brode gi brodu

**Proof of Theorem imim12d**
Step	Hyp	Ref	Expression
1		imim12d.0	. 2 ⊢ ganai broda gi ganai brode gi brodi
2		imim12d.1	. . 3 ⊢ ganai broda gi ganai brodo gi brodu
3	2	ganai-comp-rld 38	. 2 ⊢ ganai broda gi ganai ganai brodi gi brodo gi ganai brodi gi brodu
4	1, 3	syl5d 41	1 ⊢ ganai broda gi ganai ganai brodi gi brodo gi ganai brode gi brodu

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 15

This theorem is referenced by: ganai-comp-lrd 45