ganai-swap12 - brismu bridi

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Theorem ganai-swap12 29

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

**Hypothesis**
Ref	Expression
ganai-swap12.0	⊢ ganai broda gi ganai brode gi brodi

**Assertion**
Ref	Expression
ganai-swap12	⊢ ganai brode gi ganai broda gi brodi

**Proof of Theorem ganai-swap12**
Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ ganai brode gi brode
2		ganai-swap12.0	. 2 ⊢ ganai broda gi ganai brode gi brodi
3	1, 2	syl5com 28	1 ⊢ ganai brode gi 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

This theorem is referenced by: mpcom 30 mpc 31 syl5 32 ge-in-swap12 58 cur-swap12 60 uncur-swap12 62 answap 65 garid 168 subeq-lem2 451