subf - brismu bridi

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

Theorem subf 457

Description: Variables which are not free can be substituted. (Contributed by la korvo, 9-Jul-2025.)

**Hypothesis**
Ref	Expression
subf.0	⊢ na'a'u da zo'u broda

**Assertion**
Ref	Expression
subf	⊢ go [ ko'a / da ] broda gi broda

**Proof of Theorem subf**
Step	Hyp	Ref	Expression
1		subf.0	. . 3 ⊢ na'a'u da zo'u broda
2	1	nfri 439	. 2 ⊢ ganai broda gi ro da zo'u broda
3	2	subh 456	1 ⊢ go [ ko'a / da ] broda gi broda

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 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-nahahu 435 df-sub 447

This theorem is referenced by: subt 458