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Theorem mpi 31

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

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

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

**Proof of Theorem mpi**
Step	Hyp	Ref	Expression
1		mpi.0	. . 3 ⊢ broda
2	1	ki 12	. 2 ⊢ ganai brode gi broda
3		mpi.1	. 2 ⊢ ganai brode gi ganai broda gi brodi
4	2, 3	mpd 16	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

This theorem is referenced by: mp2 32