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Mirrors > Home > MPE Home > Th. List > spimvw | Structured version Visualization version GIF version |
Description: Specialization. Lemma 8 of [KalishMontague] p. 87. Uses only Tarski's FOL axiom schemes. (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 1870 | . 2 ⊢ (¬ 𝜓 → ∀𝑥 ¬ 𝜓) | |
2 | spimvw.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
3 | 1, 2 | spimw 1954 | 1 ⊢ (∀𝑥𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∀wal 1506 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1759 ax-4 1773 ax-5 1870 ax-6 1929 |
This theorem depends on definitions: df-bi 199 df-ex 1744 |
This theorem is referenced by: spvv 1956 cbvalivw 1965 alcomiw 1996 axc16i 2373 ax9ALT 2767 reu6 3622 el 5119 fvn0ssdmfun 6665 bj-el 33661 aev-o 35549 axc11next 40193 funressnvmo 42719 funressnvmoOLD 42720 |
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