syl2im - brismu bridi

	brismu bridi		< Previous Next > Nearby theorems
Mirrors > Home > Home > Th. List > syl2im

Theorem syl2im 28

Description: Replace two antecedents in parallel. (Contributed by la korvo, 31-Jul-2023.)

**Hypotheses**
Ref	Expression
syl2im.0	⊢ ganai broda gi brode
syl2im.1	⊢ ganai brodi gi brodo
syl2im.2	⊢ ganai brode gi ganai brodo gi brodu

**Assertion**
Ref	Expression
syl2im	⊢ ganai broda gi ganai brodi gi brodu

**Proof of Theorem syl2im**
Step	Hyp	Ref	Expression
1		syl2im.0	. 2 ⊢ ganai broda gi brode
2		syl2im.1	. . 3 ⊢ ganai brodi gi brodo
3		syl2im.2	. . 3 ⊢ ganai brode gi ganai brodo gi brodu
4	2, 3	syl5 27	. 2 ⊢ ganai brode gi ganai brodi gi brodu
5	1, 4	syl 18	1 ⊢ ganai broda gi ganai brodi gi brodu

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 14

This theorem is referenced by: sylc 30