mp2 - brismu bridi

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Theorem mp2 32

Description: Double modus ponens. Theorem mp2 in [ILE] p. 0. (Contributed by la korvo, 27-Jul-2023.)

**Hypotheses**
Ref	Expression
mp2.0	⊢ broda
mp2.1	⊢ brode
mp2.2	⊢ ganai broda gi ganai brode gi brodi

**Assertion**
Ref	Expression
mp2	⊢ brodi

**Proof of Theorem mp2**
Step	Hyp	Ref	Expression
1		mp2.0	. 2 ⊢ broda
2		mp2.1	. . 3 ⊢ brode
3		mp2.2	. . 3 ⊢ ganai broda gi ganai brode gi brodi
4	2, 3	mpi 31	. 2 ⊢ ganai broda 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 14

This theorem is referenced by: ge-ini 41