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Mirrors > Home > ILE Home > Th. List > cbvalv | GIF version |
Description: Rule used to change bound variables, using implicit substitition. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
cbvalv.1 | ⊢ (x = y → (φ ↔ ψ)) |
Ref | Expression |
---|---|
cbvalv | ⊢ (∀xφ ↔ ∀yψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1416 | . 2 ⊢ (φ → ∀yφ) | |
2 | ax-17 1416 | . 2 ⊢ (ψ → ∀xψ) | |
3 | cbvalv.1 | . 2 ⊢ (x = y → (φ ↔ ψ)) | |
4 | 1, 2, 3 | cbvalh 1633 | 1 ⊢ (∀xφ ↔ ∀yψ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 98 ∀wal 1240 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 |
This theorem depends on definitions: df-bi 110 df-nf 1347 |
This theorem is referenced by: nfcjust 2163 cdeqal1 2749 zfpow 3919 tfisi 4253 acexmid 5454 tfrlem3-2d 5869 tfrlemi1 5887 tfrexlem 5889 genprndl 6504 genprndu 6505 |
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