ga-pairl - brismu bridi

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Theorem ga-pairl 180

Description: ga-pair 179 with the arrow on the left. (Contributed by la korvo, 14-Jul-2025.)

**Hypothesis**
Ref	Expression
ga-pairx.0	⊢ ganai broda gi brode

**Assertion**
Ref	Expression
ga-pairl	⊢ ganai ga broda gi brodi gi ga brode gi brodi

**Proof of Theorem ga-pairl**
Step	Hyp	Ref	Expression
1		ga-pairx.0	. 2 ⊢ ganai broda gi brode
2		id 19	. 2 ⊢ ganai brodi gi brodi
3	1, 2	ga-pair 179	1 ⊢ ganai ga broda gi brodi gi ga brode gi brodi

Colors of variables: sumti selbri bridi

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-le 48 ax-ge-re 49 ax-ge-in 50

This theorem depends on definitions: df-go 83 df-ga 161

This theorem is referenced by: (None)