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Mirrors > Home > MPE Home > Th. List > sbf2 | Structured version Visualization version GIF version |
Description: Substitution has no effect on a bound variable. (Contributed by NM, 1-Jul-2005.) |
Ref | Expression |
---|---|
sbf2 | ⊢ ([𝑦 / 𝑥]∀𝑥𝜑 ↔ ∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 2015 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | 1 | sbf 2368 | 1 ⊢ ([𝑦 / 𝑥]∀𝑥𝜑 ↔ ∀𝑥𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 ∀wal 1473 [wsb 1867 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-ex 1696 df-nf 1701 df-sb 1868 |
This theorem is referenced by: (None) |
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