ge-ini - brismu bridi

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Theorem ge-ini 55

Description: Inference form of ax-ge-in 50 (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 50	. 2 ⊢ ganai broda gi ganai brode gi ge broda gi brode
4	1, 2, 3	mp2 37	1 ⊢ ge broda gi brode

Colors of variables: sumti selbri bridi

Syntax hints: ge bge 47

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-in 50

This theorem is referenced by: iso 87 giherii 159 pameiii 330 simsarii 363 stecirii 386 muplirii 393 fahuri 533 nat-indii 602 kazmi-funii 635 pagbu-antisym 646 pagbu-trans 648