mpan2 - brismu bridi

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Theorem mpan2 74

Description: An inference eliminating a conjunction from the antecedent. (Contributed by la korvo, 8-Jul-2025.)

**Hypotheses**
Ref	Expression
mpan2.0	⊢ brode
mpan2.1	⊢ ganai ge broda gi brode gi brodi

**Assertion**
Ref	Expression
mpan2	⊢ ganai broda gi brodi

**Proof of Theorem mpan2**
Step	Hyp	Ref	Expression
1		mpan2.0	. . 3 ⊢ brode
2	1	ki 12	. 2 ⊢ ganai broda gi brode
3		mpan2.1	. 2 ⊢ ganai ge broda gi brode gi brodi
4	2, 3	mpdan 72	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 50

This theorem is referenced by: equs4 453