mpd - brismu bridi

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Theorem mpd 18

Description: Deductive form of ax-mp 10 (Contributed by la korvo, 27-Jul-2023.)

**Hypotheses**
Ref	Expression
mpd.0	⊢ ganai broda gi brode
mpd.1	⊢ ganai broda gi ganai brode gi brodi

**Assertion**
Ref	Expression
mpd	⊢ ganai broda gi brodi

**Proof of Theorem mpd**
Step	Hyp	Ref	Expression
1		mpd.0	. 2 ⊢ ganai broda gi brode
2		mpd.1	. . 3 ⊢ ganai broda gi ganai brode gi brodi
3	2	si 16	. 2 ⊢ ganai ganai broda gi brode gi ganai broda gi brodi
4	1, 3	ax-mp 10	1 ⊢ ganai broda gi brodi

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9

This theorem was proved from axioms: ax-mp 10 ax-s 15

This theorem is referenced by: id 19 syl 21 mpdd 23 mpcom 30 ganai-abs 34 mpi 36 mt2d 290