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Theorem mpan 49

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

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

**Assertion**
Ref	Expression
mpan	⊢ ganai brode gi brodi

**Proof of Theorem mpan**
Step	Hyp	Ref	Expression
1		mpan.0	. . 3 ⊢ broda
2	1	ki 12	. 2 ⊢ ganai brode gi broda
3		mpan.1	. 2 ⊢ ganai ge broda gi brode gi brodi
4	2, 3	mpancom 48	1 ⊢ ganai brode gi brodi

Colors of variables: sumti selbri bridi

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 14 ax-ge-in 36

This theorem is referenced by: mp2an 50