mpancom - brismu bridi

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Theorem mpancom 57

Description: A variant of mpan 58 (Contributed by la korvo, 31-Jul-2023.)

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

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

**Proof of Theorem mpancom**
Step	Hyp	Ref	Expression
1		mpancom.0	. 2 ⊢ ganai broda gi brode
2		id 18	. 2 ⊢ ganai broda gi broda
3		mpancom.1	. 2 ⊢ ganai ge brode gi broda gi brodi
4	1, 2, 3	syl2anc 56	1 ⊢ ganai broda gi brodi

Colors of variables: sumti selbri bridi

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

This theorem is referenced by: mpan 58