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Mirrors > Home > MPE Home > Th. List > sbequ5 | Structured version Visualization version GIF version |
Description: Substitution does not change an identical variable specifier. Usage of this theorem is discouraged because it depends on ax-13 2371. (Contributed by NM, 15-May-1993.) (New usage is discouraged.) |
Ref | Expression |
---|---|
sbequ5 | ⊢ ([𝑤 / 𝑧]∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥 𝑥 = 𝑦) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfae 2432 | . 2 ⊢ Ⅎ𝑧∀𝑥 𝑥 = 𝑦 | |
2 | 1 | sbf 2263 | 1 ⊢ ([𝑤 / 𝑧]∀𝑥 𝑥 = 𝑦 ↔ ∀𝑥 𝑥 = 𝑦) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∀wal 1540 [wsb 2068 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-10 2138 ax-11 2155 ax-12 2172 ax-13 2371 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-ex 1783 df-nf 1787 df-sb 2069 |
This theorem is referenced by: (None) |
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