uncur - brismu bridi

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Theorem uncur 45

Description: The natural uncurry (or "export") for any well-formed statement. Theorem ex in [ILE] p. 0. (Contributed by la korvo, 31-Jul-2023.)

**Hypothesis**
Ref	Expression
uncur.0	⊢ ganai ge broda gi brode gi brodi

**Assertion**
Ref	Expression
uncur	⊢ ganai broda gi ganai brode gi brodi

**Proof of Theorem uncur**
Step	Hyp	Ref	Expression
1		ax-ge-in 36	. 2 ⊢ ganai broda gi ganai brode gi ge broda gi brode
2		uncur.0	. 2 ⊢ ganai ge broda gi brode gi brodi
3	1, 2	syl6 22	1 ⊢ ganai broda gi ganai brode gi brodi

Colors of variables: sumti selbri bridi

Syntax hints: ge bge 33

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 14 ax-ge-in 36

This theorem is referenced by: syl2anc 47 bi3 59 subeq-lem1 353 nat-ind-cur 493