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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-nfnae1 | Structured version Visualization version GIF version |
Description: Unlike nfnae 2306, this specialized theorem avoids ax-11 2021. (Contributed by Wolf Lammen, 27-Jun-2019.) |
Ref | Expression |
---|---|
wl-nfnae1 | ⊢ Ⅎ𝑥 ¬ ∀𝑦 𝑦 = 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-nfae1 32494 | . 2 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥 | |
2 | 1 | nfn 1768 | 1 ⊢ Ⅎ𝑥 ¬ ∀𝑦 𝑦 = 𝑥 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∀wal 1473 Ⅎwnf 1699 |
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-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 |
This theorem is referenced by: wl-cbvalnaed 32498 wl-2sb6d 32520 |
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