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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 2154. (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 2148 | . 2 ⊢ Ⅎ𝑥∀𝑥 𝑥 = 𝑦 | |
3 | 1, 2 | nfxfr 1855 | 1 ⊢ Ⅎ𝑥∀𝑦 𝑦 = 𝑥 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1537 Ⅎwnf 1786 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-10 2137 ax-12 2171 ax-13 2372 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-ex 1783 df-nf 1787 |
This theorem is referenced by: wl-nfnae1 35687 |
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