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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-bialal | Structured version Visualization version GIF version |
Description: When 𝜑 is substituted for 𝜓, both sides express a form of nonfreeness. (Contributed by BJ, 20-Oct-2019.) |
Ref | Expression |
---|---|
bj-bialal | ⊢ (∀𝑥(∀𝑥𝜑 → 𝜓) ↔ (∀𝑥𝜑 → ∀𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2146 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | 1 | 19.21 2197 | 1 ⊢ (∀𝑥(∀𝑥𝜑 → 𝜓) ↔ (∀𝑥𝜑 → ∀𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 207 ∀wal 1526 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-10 2136 ax-12 2167 |
This theorem depends on definitions: df-bi 208 df-or 842 df-ex 1772 df-nf 1776 |
This theorem is referenced by: (None) |
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