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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-nfae1 | Structured version Visualization version GIF version |
Description: Unlike nfae 2433, this specialized theorem avoids ax-11 2162. (Contributed by Wolf Lammen, 26-Jun-2019.) |
Ref | Expression |
---|---|
wl-nfae1 | ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aecom 2427 | . 2 ⊢ (∀𝑦 𝑦 = 𝑥 ↔ ∀𝑥 𝑥 = 𝑦) | |
2 | nfa1 2156 | . 2 ⊢ Ⅎ𝑥∀𝑥 𝑥 = 𝑦 | |
3 | 1, 2 | nfxfr 1859 | 1 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1540 Ⅎwnf 1790 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-10 2145 ax-12 2179 ax-13 2372 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 df-ex 1787 df-nf 1791 |
This theorem is referenced by: wl-nfnae1 35310 |
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