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Mirrors > Home > MPE Home > Th. List > mo4OLD | Structured version Visualization version GIF version |
Description: Obsolete version of mo4 2649 as of 18-Oct-2023. (Contributed by NM, 26-Jul-1995.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
mo4OLD.1 | ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) |
Ref | Expression |
---|---|
mo4OLD | ⊢ (∃*𝑥𝜑 ↔ ∀𝑥∀𝑦((𝜑 ∧ 𝜓) → 𝑥 = 𝑦)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1914 | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | mo4OLD.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 ↔ 𝜓)) | |
3 | 1, 2 | mo4f 2650 | 1 ⊢ (∃*𝑥𝜑 ↔ ∀𝑥∀𝑦((𝜑 ∧ 𝜓) → 𝑥 = 𝑦)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 208 ∧ wa 398 ∀wal 1534 ∃*wmo 2619 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-10 2144 ax-11 2160 ax-12 2176 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-mo 2621 |
This theorem is referenced by: (None) |
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