mp2an - brismu bridi

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Theorem mp2an 75

Description: An inference eliminating a conjunction from the antecedent. (Contributed by la korvo, 31-Jul-2023.)

**Hypotheses**
Ref	Expression
mp2an.0	⊢ broda
mp2an.1	⊢ brode
mp2an.2	⊢ ganai ge broda gi brode gi brodi

**Assertion**
Ref	Expression
mp2an	⊢ brodi

**Proof of Theorem mp2an**
Step	Hyp	Ref	Expression
1		mp2an.1	. 2 ⊢ brode
2		mp2an.0	. . 3 ⊢ broda
3		mp2an.2	. . 3 ⊢ ganai ge broda gi brode gi brodi
4	2, 3	mpan 73	. 2 ⊢ ganai brode gi brodi
5	1, 4	ax-mp 10	1 ⊢ 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 50

This theorem is referenced by: ga-sum 167