eximdh - brismu bridi

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Theorem eximdh 430

Description: Deductive form of exim 428 (Contributed by la korvo, 9-Jul-2025.)

**Hypotheses**
Ref	Expression
eximdh.0	⊢ ganai broda gi ro da zo'u broda
eximdh.1	⊢ ganai broda gi ganai brode gi brodi

**Assertion**
Ref	Expression
eximdh	⊢ ganai broda gi ganai su'o da zo'u brode gi su'o da zo'u brodi

**Proof of Theorem eximdh**
Step	Hyp	Ref	Expression
1		eximdh.0	. . 3 ⊢ ganai broda gi ro da zo'u broda
2		eximdh.1	. . 3 ⊢ ganai broda gi ganai brode gi brodi
3	1, 2	alrimih 238	. 2 ⊢ ganai broda gi ro da zo'u ganai brode gi brodi
4		exim 428	. 2 ⊢ ganai ro da zo'u ganai brode gi brodi gi ganai su'o da zo'u brode gi su'o da zo'u brodi
5	3, 4	syl 21	1 ⊢ ganai broda gi ganai su'o da zo'u brode gi su'o da zo'u brodi

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9 ro brd 222 su'o bsd 416

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-le 48 ax-ge-re 49 ax-ge-in 50 ax-gen1 224 ax-spec1 228 ax-qi1 234 ax-ro1-nf 249 ax-eb 420 ax-eq 422

This theorem depends on definitions: df-go 83

This theorem is referenced by: foml19.41 434