syl2anc - brismu bridi

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Theorem syl2anc 70

Description: A contracting syllogism. (Contributed by la korvo, 31-Jul-2023.)

**Hypotheses**
Ref	Expression
syl2anc.0	⊢ ganai broda gi brode
syl2anc.1	⊢ ganai broda gi brodi
syl2anc.2	⊢ ganai ge brode gi brodi gi brodo

**Assertion**
Ref	Expression
syl2anc	⊢ ganai broda gi brodo

**Proof of Theorem syl2anc**
Step	Hyp	Ref	Expression
1		syl2anc.0	. 2 ⊢ ganai broda gi brode
2		syl2anc.1	. 2 ⊢ ganai broda gi brodi
3		syl2anc.2	. . 3 ⊢ ganai ge brode gi brodi gi brodo
4	3	uncur 61	. 2 ⊢ ganai brode gi ganai brodi gi brodo
5	1, 2, 4	sylc 35	1 ⊢ ganai broda gi brodo

Colors of variables: sumti selbri bridi

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-in 50

This theorem is referenced by: mpancom 71 mpdan 72