ganai-swap23 - brismu bridi

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Theorem ganai-swap23 43

Description: Naturally swap the second and third antecedents in an internalized inference. (Contributed by la korvo, 30-Jul-2023.)

**Hypothesis**
Ref	Expression
ganai-swap23.0	⊢ ganai broda gi ganai brode gi ganai brodi gi brodo

**Assertion**
Ref	Expression
ganai-swap23	⊢ ganai broda gi ganai brodi gi ganai brode gi brodo

**Proof of Theorem ganai-swap23**
Step	Hyp	Ref	Expression
1		ganai-swap23.0	. 2 ⊢ ganai broda gi ganai brode gi ganai brodi gi brodo
2		mpc 31	. 2 ⊢ ganai brodi gi ganai ganai brodi gi brodo gi brodo
3	1, 2	syl9 42	1 ⊢ ganai broda gi ganai brodi gi ganai brode gi brodo

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15

This theorem is referenced by: con2d 289