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Theorem subid 355

Description: An identity for substitutions. Theorem sbid in [ILE] p. 0. (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 202	. . 3 ⊢ da du da
2		subeq-lem1 353	. . . 4 ⊢ ganai da du da gi ganai broda gi [ da / da ] broda
3		subeq-lem2 354	. . . 4 ⊢ ganai da du da gi ganai [ da / da ] broda gi broda
4	2, 3	isod 62	. . 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 66	1 ⊢ go [ da / da ] broda gi broda

Colors of variables: sumti selbri bridi

Syntax hints: go bgo 51 du sbdu 196 [ bsub 349

This theorem was proved from axioms: ax-mp 10 ax-k 11 ax-s 14 ax-ge-le 34 ax-ge-re 35 ax-ge-in 36 ax-gen1 179 ax-gen2 180 ax-spec1 181 ax-qi2 188 ax-eb 343 ax-eq 345

This theorem depends on definitions: df-go 52 df-o 153 df-du 197 df-sub 350

This theorem is referenced by: (None)