mpcom - brismu bridi

	brismu bridi		< Previous Next > Nearby theorems
Mirrors > Home > Home > Th. List > mpcom

Theorem mpcom 30

Description: Remove a duplicated antecedent from an inference. (Contributed by la korvo, 8-Jul-2025.)

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

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

**Proof of Theorem mpcom**
Step	Hyp	Ref	Expression
1		mpcom.0	. 2 ⊢ ganai broda gi brode
2		mpcom.1	. . 3 ⊢ ganai brode gi ganai broda gi brodi
3	2	ganai-swap12 29	. 2 ⊢ ganai broda gi ganai brode gi brodi
4	1, 3	mpd 18	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

This theorem is referenced by: syldan 66