stdpc4 - brismu bridi

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Theorem stdpc4 455

Description: The Axiom of Specialization: if a statement holds for all values, then it holds when substituted for any particular value. (Contributed by la korvo, 9-Jul-2025.)

**Assertion**
Ref	Expression
stdpc4	⊢ ganai ro da zo'u broda gi [ ko'a / da ] broda

**Proof of Theorem stdpc4**
Step	Hyp	Ref	Expression
1		ax-k 11	. . 3 ⊢ ganai broda gi ganai da du ko'a gi broda
2	1	qi1q 237	. 2 ⊢ ganai ro da zo'u broda gi ro da zo'u ganai da du ko'a gi broda
3		sub2 454	. 2 ⊢ ganai ro da zo'u ganai da du ko'a gi broda gi [ ko'a / da ] broda
4	2, 3	syl 21	1 ⊢ ganai ro da zo'u broda gi [ ko'a / da ] broda

Colors of variables: sumti selbri bridi

Syntax hints: ganai bgan 9 ro brd 222 du sbdu 250 [ bsub 446

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 ax-gen1 224 ax-spec1 228 ax-qi1 234 ax-ro1-nf 249 ax-ex 416 ax-eb 418 ax-eq 420

This theorem depends on definitions: df-go 83 df-sub 447

This theorem is referenced by: subh 456

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