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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 123 | . 2 ⊢ (𝜓 ↔ 𝜒) |
4 | 1, 3 | xchbinx 607 | 1 ⊢ (𝜑 ↔ ¬ 𝜒) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ↔ wb 98 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: xordc1 1284 sbnv 1768 ralnex 2316 difab 3206 disjsn 3432 iindif2m 3724 reldm0 4553 |
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