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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 40741 | . 2 ⊢ (∃!𝑥𝜑 → (℩𝑥𝜑) ∈ V) | |
2 | spsbc 3783 | . 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 1529 ∈ wcel 2108 ∃!weu 2647 Vcvv 3493 [wsbc 3770 ℩cio 6305 |
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 1905 ax-6 1964 ax-7 2009 ax-8 2110 ax-9 2118 ax-10 2139 ax-11 2154 ax-12 2170 ax-ext 2791 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1534 df-ex 1775 df-nf 1779 df-sb 2064 df-mo 2616 df-eu 2648 df-clab 2798 df-cleq 2812 df-clel 2891 df-nfc 2961 df-rex 3142 df-v 3495 df-sbc 3771 df-un 3939 df-sn 4560 df-pr 4562 df-uni 4831 df-iota 6307 |
This theorem is referenced by: (None) |
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