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Mirrors > Home > MPE Home > Th. List > sbequ6 | Structured version Visualization version GIF version |
Description: Substitution does not change a distinctor. Usage of this theorem is discouraged because it depends on ax-13 2367. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.) |
Ref | Expression |
---|---|
sbequ6 | ⊢ ([𝑤 / 𝑧] ¬ ∀𝑥 𝑥 = 𝑦 ↔ ¬ ∀𝑥 𝑥 = 𝑦) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnae 2429 | . 2 ⊢ Ⅎ𝑧 ¬ ∀𝑥 𝑥 = 𝑦 | |
2 | 1 | sbf 2258 | 1 ⊢ ([𝑤 / 𝑧] ¬ ∀𝑥 𝑥 = 𝑦 ↔ ¬ ∀𝑥 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 205 ∀wal 1532 [wsb 2060 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-10 2130 ax-11 2147 ax-12 2167 ax-13 2367 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-tru 1537 df-ex 1775 df-nf 1779 df-sb 2061 |
This theorem is referenced by: (None) |
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