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Mirrors > Home > MPE Home > Th. List > Mathboxes > nfich2 | Structured version Visualization version GIF version |
Description: The second interchangeable setvar variable is not free. (Contributed by AV, 21-Aug-2023.) |
Ref | Expression |
---|---|
nfich2 | ⊢ Ⅎ𝑦[𝑥⇄𝑦]𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ich 43681 | . 2 ⊢ ([𝑥⇄𝑦]𝜑 ↔ ∀𝑥∀𝑦([𝑥 / 𝑎][𝑦 / 𝑥][𝑎 / 𝑦]𝜑 ↔ 𝜑)) | |
2 | nfa2 2175 | . 2 ⊢ Ⅎ𝑦∀𝑥∀𝑦([𝑥 / 𝑎][𝑦 / 𝑥][𝑎 / 𝑦]𝜑 ↔ 𝜑) | |
3 | 1, 2 | nfxfr 1852 | 1 ⊢ Ⅎ𝑦[𝑥⇄𝑦]𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 208 ∀wal 1534 Ⅎwnf 1783 [wsb 2068 [wich 43680 |
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-10 2144 ax-11 2160 |
This theorem depends on definitions: df-bi 209 df-or 844 df-ex 1780 df-nf 1784 df-ich 43681 |
This theorem is referenced by: ich2exprop 43703 ichreuopeq 43705 |
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