subid - brismu bridi

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Theorem subid 394

Description: An identity for substitutions. (Contributed by la korvo, 22-Jun-2024.)

**Assertion**
Ref	Expression
subid	⊢ go [ da / da ] broda gi broda

**Proof of Theorem subid**
Step	Hyp	Ref	Expression
1		du-refl 220	. . 3 ⊢ da du da
2		subeq-lem1 392	. . . 4 ⊢ ganai da du da gi ganai broda gi [ da / da ] broda
3		subeq-lem2 393	. . . 4 ⊢ ganai da du da gi ganai [ da / da ] broda gi broda
4	2, 3	isod 72	. . 3 ⊢ ganai da du da gi go broda gi [ da / da ] broda
5	1, 4	ax-mp 10	. 2 ⊢ go broda gi [ da / da ] broda
6	5	go-comi 76	1 ⊢ go [ da / da ] broda gi broda

Colors of variables: sumti selbri bridi

Syntax hints: go bgo 60 du sbdu 214 [ bsub 388

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 15 ax-ge-le 43 ax-ge-re 44 ax-ge-in 45 ax-gen1 193 ax-gen2 195 ax-spec1 196 ax-qi2 204 ax-eb 381 ax-eq 383

This theorem depends on definitions: df-go 61 df-o 167 df-du 215 df-sub 389

This theorem is referenced by: (None)