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Mirrors > Home > MPE Home > Th. List > Mathboxes > ich2al | Structured version Visualization version GIF version |
Description: Two setvar variables are always interchangeable when there are two universal quantifiers. (Contributed by SN, 23-Nov-2023.) |
Ref | Expression |
---|---|
ich2al | ⊢ [𝑥⇄𝑦]∀𝑥∀𝑦𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2154 | . 2 ⊢ Ⅎ𝑥∀𝑥∀𝑦𝜑 | |
2 | nfa2 2175 | . 2 ⊢ Ⅎ𝑦∀𝑥∀𝑦𝜑 | |
3 | 1, 2 | ichf 43685 | 1 ⊢ [𝑥⇄𝑦]∀𝑥∀𝑦𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1534 [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-5 1910 ax-6 1969 ax-7 2014 ax-10 2144 ax-11 2160 ax-12 2176 |
This theorem depends on definitions: df-bi 209 df-or 844 df-ex 1780 df-nf 1784 df-sb 2069 df-ich 43681 |
This theorem is referenced by: (None) |
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