Mathbox for Andrew Salmon |
< Previous
Next >
Nearby theorems |
||
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 37641 | . 2 ⊢ (∃!𝑥𝜑 → (℩𝑥𝜑) ∈ V) | |
2 | spsbc 3415 | . 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 1473 ∈ wcel 1977 ∃!weu 2458 Vcvv 3173 [wsbc 3402 ℩cio 5766 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-eu 2462 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rex 2902 df-v 3175 df-sbc 3403 df-un 3545 df-sn 4126 df-pr 4128 df-uni 4373 df-iota 5768 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |