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Mirrors > Home > MPE Home > Th. List > cbvalivw | Structured version Visualization version GIF version |
Description: Change bound variable. Uses only Tarski's FOL axiom schemes. Part of Lemma 7 of [KalishMontague] p. 86. (Contributed by NM, 9-Apr-2017.) |
Ref | Expression |
---|---|
cbvalivw.1 | ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
cbvalivw | ⊢ (∀𝑥𝜑 → ∀𝑦𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvalivw.1 | . . 3 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
2 | 1 | spimvw 2002 | . 2 ⊢ (∀𝑥𝜑 → 𝜓) |
3 | 2 | alrimiv 1928 | 1 ⊢ (∀𝑥𝜑 → ∀𝑦𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1536 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 |
This theorem depends on definitions: df-bi 210 df-ex 1782 |
This theorem is referenced by: alcomiwOLD 2051 cbvaev 2058 wl-cbvmotv 34918 axc11next 41110 |
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