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Mirrors > Home > MPE Home > Th. List > Mathboxes > nfich1 | Structured version Visualization version GIF version |
Description: The first interchangeable setvar variable is not free. (Contributed by AV, 21-Aug-2023.) |
Ref | Expression |
---|---|
nfich1 | ⊢ Ⅎ𝑥[𝑥⇄𝑦]𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ich 43655 | . 2 ⊢ ([𝑥⇄𝑦]𝜑 ↔ ∀𝑥∀𝑦([𝑥 / 𝑎][𝑦 / 𝑥][𝑎 / 𝑦]𝜑 ↔ 𝜑)) | |
2 | nfa1 2155 | . 2 ⊢ Ⅎ𝑥∀𝑥∀𝑦([𝑥 / 𝑎][𝑦 / 𝑥][𝑎 / 𝑦]𝜑 ↔ 𝜑) | |
3 | 1, 2 | nfxfr 1853 | 1 ⊢ Ⅎ𝑥[𝑥⇄𝑦]𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∀wal 1535 Ⅎwnf 1784 [wsb 2069 [wich 43654 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-10 2145 |
This theorem depends on definitions: df-bi 209 df-or 844 df-ex 1781 df-nf 1785 df-ich 43655 |
This theorem is referenced by: ichnfim 43673 ich2exprop 43682 ichreuopeq 43684 |
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