ge-ini - brismu bridi

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Theorem ge-ini 50

Description: Inference form of ax-ge-in 45 (Contributed by la korvo, 27-Jul-2023.)

**Hypotheses**
Ref	Expression
ge-ini.0	⊢ broda
ge-ini.1	⊢ brode

**Assertion**
Ref	Expression
ge-ini	⊢ ge broda gi brode

**Proof of Theorem ge-ini**
Step	Hyp	Ref	Expression
1		ge-ini.0	. 2 ⊢ broda
2		ge-ini.1	. 2 ⊢ brode
3		ax-ge-in 45	. 2 ⊢ ganai broda gi ganai brode gi ge broda gi brode
4	1, 2, 3	mp2 35	1 ⊢ ge broda gi brode

Colors of variables: sumti selbri bridi

Syntax hints: ge bge 42

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-in 45

This theorem is referenced by: iso 65 giherii 136 pameiii 292 simsarii 325 stecirii 347 muplirii 354 fahuri 473 nat-indii 534 kazmi-funii 565 pagbu-antisym 571 pagbu-trans 573