| Mathbox for Giovanni Mascellani |
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| Mirrors > Home > MPE Home > Th. List > Mathboxes > sbfal | Structured version Visualization version GIF version | ||
| Description: Substitution does not change falsity. (Contributed by Giovanni Mascellani, 24-May-2019.) |
| Ref | Expression |
|---|---|
| sbfal.1 | ⊢ 𝐴 ∈ V |
| Ref | Expression |
|---|---|
| sbfal | ⊢ ([𝐴 / 𝑥]⊥ ↔ ⊥) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbfal.1 | . 2 ⊢ 𝐴 ∈ V | |
| 2 | sbcg 3863 | . 2 ⊢ (𝐴 ∈ V → ([𝐴 / 𝑥]⊥ ↔ ⊥)) | |
| 3 | 1, 2 | ax-mp 5 | 1 ⊢ ([𝐴 / 𝑥]⊥ ↔ ⊥) |
| Colors of variables: wff setvar class |
| Syntax hints: ↔ wb 206 ⊥wfal 1552 ∈ wcel 2108 Vcvv 3480 [wsbc 3788 |
| 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 1967 ax-7 2007 ax-8 2110 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-sb 2065 df-clab 2715 df-clel 2816 df-sbc 3789 |
| This theorem is referenced by: (None) |
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