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Mirrors > Home > ILE Home > Th. List > 19.36aiv | GIF version |
Description: Inference from Theorem 19.36 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
19.36aiv.1 | ⊢ ∃𝑥(𝜑 → 𝜓) |
Ref | Expression |
---|---|
19.36aiv | ⊢ (∀𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1539 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | 19.36aiv.1 | . 2 ⊢ ∃𝑥(𝜑 → 𝜓) | |
3 | 1, 2 | 19.36i 1683 | 1 ⊢ (∀𝑥𝜑 → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1362 ∃wex 1503 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-4 1521 ax-17 1537 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 |
This theorem is referenced by: vtocl2 2807 vtocl3 2808 |
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