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Mirrors > Home > ILE Home > Th. List > xchbinxr | GIF version |
Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.) |
Ref | Expression |
---|---|
xchbinxr.1 | ⊢ (𝜑 ↔ ¬ 𝜓) |
xchbinxr.2 | ⊢ (𝜒 ↔ 𝜓) |
Ref | Expression |
---|---|
xchbinxr | ⊢ (𝜑 ↔ ¬ 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xchbinxr.1 | . 2 ⊢ (𝜑 ↔ ¬ 𝜓) | |
2 | xchbinxr.2 | . . 3 ⊢ (𝜒 ↔ 𝜓) | |
3 | 2 | bicomi 130 | . 2 ⊢ (𝜓 ↔ 𝜒) |
4 | 1, 3 | xchbinx 640 | 1 ⊢ (𝜑 ↔ ¬ 𝜒) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: xordc1 1325 sbnv 1811 ralnex 2363 difab 3249 disjsn 3472 iindif2m 3765 reldm0 4601 |
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