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Mirrors > Home > MPE Home > Th. List > spimvw | Structured version Visualization version GIF version |
Description: A weak form of specialization. Lemma 8 of [KalishMontague] p. 87. Uses only Tarski's FOL axiom schemes. For stronger forms using more axioms, see spimv 2385 and spimfv 2228. (Contributed by NM, 9-Apr-2017.) |
Ref | Expression |
---|---|
spimvw.1 | ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
spimvw | ⊢ (∀𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-5 1906 | . 2 ⊢ (¬ 𝜓 → ∀𝑥 ¬ 𝜓) | |
2 | spimvw.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
3 | 1, 2 | spimw 1967 | 1 ⊢ (∀𝑥𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1532 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 |
This theorem depends on definitions: df-bi 206 df-ex 1775 |
This theorem is referenced by: spvv 1993 cbvalivw 2003 alcomiw 2039 axc16i 2431 ax9ALT 2723 reu6 3721 disj 4448 elALT2 5369 fvn0ssdmfun 7084 aev-o 38403 axc11next 43843 funressnvmo 46427 |
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