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Mirrors > Home > MPE Home > Th. List > Mathboxes > pm14.18 | Structured version Visualization version GIF version |
Description: Theorem *14.18 in [WhiteheadRussell] p. 189. (Contributed by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
pm14.18 | ⊢ (∃!𝑥𝜑 → (∀𝑥𝜓 → [(℩𝑥𝜑) / 𝑥]𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iotaexeu 44373 | . 2 ⊢ (∃!𝑥𝜑 → (℩𝑥𝜑) ∈ V) | |
2 | spsbc 3804 | . 2 ⊢ ((℩𝑥𝜑) ∈ V → (∀𝑥𝜓 → [(℩𝑥𝜑) / 𝑥]𝜓)) | |
3 | 1, 2 | syl 17 | 1 ⊢ (∃!𝑥𝜑 → (∀𝑥𝜓 → [(℩𝑥𝜑) / 𝑥]𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1533 ∈ wcel 2104 ∃!weu 2564 Vcvv 3477 [wsbc 3791 ℩cio 6508 |
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 1963 ax-7 2003 ax-8 2106 ax-9 2114 ax-10 2137 ax-12 2173 ax-ext 2704 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 847 df-tru 1538 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2536 df-eu 2565 df-clab 2711 df-cleq 2725 df-clel 2812 df-v 3479 df-sbc 3792 df-un 3968 df-ss 3980 df-sn 4631 df-pr 4633 df-uni 4915 df-iota 6510 |
This theorem is referenced by: (None) |
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