| Mathbox for Wolf Lammen |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-nfae1 | Structured version Visualization version GIF version | ||
| Description: Unlike nfae 2438, this specialized theorem avoids ax-11 2157. (Contributed by Wolf Lammen, 26-Jun-2019.) |
| Ref | Expression |
|---|---|
| wl-nfae1 | ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | aecom 2432 | . 2 ⊢ (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦) | |
| 2 | nfa1 2151 | . 2 ⊢ Ⅎ𝑥∀𝑥 𝑥 = 𝑦 | |
| 3 | 1, 2 | nfxfr 1853 | 1 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥 |
| Colors of variables: wff setvar class |
| Syntax hints: ∀wal 1538 Ⅎwnf 1783 |
| 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 1967 ax-7 2007 ax-10 2141 ax-12 2177 ax-13 2377 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-ex 1780 df-nf 1784 |
| This theorem is referenced by: wl-nfnae1 37529 |
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