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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 3870 | . 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 1549 ∈ wcel 2106 Vcvv 3478 [wsbc 3791 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 |
This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1777 df-sb 2063 df-clab 2713 df-clel 2814 df-sbc 3792 |
This theorem is referenced by: (None) |
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