jca - brismu bridi

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Theorem jca 46

Description: "Join Consequents with AND". (Contributed by la korvo, 22-Jun-2024.)

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

**Assertion**
Ref	Expression
jca	⊢ ganai broda gi ge brode gi brodi

**Proof of Theorem jca**
Step	Hyp	Ref	Expression
1		jca.0	. 2 ⊢ ganai broda gi brode
2		jca.1	. 2 ⊢ ganai broda gi brodi
3		ax-ge-in 36	. 2 ⊢ ganai brode gi ganai brodi gi ge brode gi brodi
4	1, 2, 3	sylc 30	1 ⊢ ganai broda gi ge 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: sylanbrc 75