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Mirrors > Home > ILE Home > Th. List > xchnxbir | GIF version |
Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.) |
Ref | Expression |
---|---|
xchnxbir.1 | ⊢ (¬ 𝜑 ↔ 𝜓) |
xchnxbir.2 | ⊢ (𝜒 ↔ 𝜑) |
Ref | Expression |
---|---|
xchnxbir | ⊢ (¬ 𝜒 ↔ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xchnxbir.1 | . 2 ⊢ (¬ 𝜑 ↔ 𝜓) | |
2 | xchnxbir.2 | . . 3 ⊢ (𝜒 ↔ 𝜑) | |
3 | 2 | bicomi 131 | . 2 ⊢ (𝜑 ↔ 𝜒) |
4 | 1, 3 | xchnxbi 641 | 1 ⊢ (¬ 𝜒 ↔ 𝜓) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 104 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: 3ioran 940 truxortru 1356 truxorfal 1357 falxortru 1358 falxorfal 1359 intirr 4833 hashunlem 10275 |
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