ga-sum - brismu bridi

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Theorem ga-sum 167

Description: All binary coproducts exist. (Contributed by la korvo, 31-Jul-2023.)

**Hypotheses**
Ref	Expression
ga-sum.0	⊢ ganai broda gi brode
ga-sum.1	⊢ ganai brodi gi brode

**Assertion**
Ref	Expression
ga-sum	⊢ ganai ga broda gi brodi gi brode

**Proof of Theorem ga-sum**
Step	Hyp	Ref	Expression
1		ga-sum.0	. 2 ⊢ ganai broda gi brode
2		ga-sum.1	. 2 ⊢ ganai brodi gi brode
3		gar 163	. 2 ⊢ ganai ge ganai broda gi brode gi ganai brodi gi brode gi ganai ga broda gi brodi gi brode
4	1, 2, 3	mp2an 75	1 ⊢ ganai ga broda gi brodi gi brode

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9 ga bga 160

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

This theorem depends on definitions: df-go 83 df-ga 161

This theorem is referenced by: garid 168 garian 170 ga-idem 171 ga-com-lem 172 ge-dist-ga 174 ga-pair 179