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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 2389 and spimfv 2237. (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 1918 | . 2 ⊢ (¬ 𝜓 → ∀𝑥 ¬ 𝜓) | |
2 | spimvw.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
3 | 1, 2 | spimw 1979 | 1 ⊢ (∀𝑥𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1541 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 |
This theorem depends on definitions: df-bi 210 df-ex 1788 |
This theorem is referenced by: spvv 2005 cbvalivw 2015 alcomiw 2051 alcomiwOLD 2052 axc16i 2435 ax9ALT 2732 reu6 3639 disj 4362 el 5262 fvn0ssdmfun 6895 aev-o 36682 axc11next 41697 funressnvmo 44211 |
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