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Mirrors > Home > ILE Home > Th. List > orbi1i | GIF version |
Description: Inference adding a right disjunct to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
orbi2i.1 | ⊢ (φ ↔ ψ) |
Ref | Expression |
---|---|
orbi1i | ⊢ ((φ ∨ χ) ↔ (ψ ∨ χ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orcom 646 | . 2 ⊢ ((φ ∨ χ) ↔ (χ ∨ φ)) | |
2 | orbi2i.1 | . . 3 ⊢ (φ ↔ ψ) | |
3 | 2 | orbi2i 678 | . 2 ⊢ ((χ ∨ φ) ↔ (χ ∨ ψ)) |
4 | orcom 646 | . 2 ⊢ ((χ ∨ ψ) ↔ (ψ ∨ χ)) | |
5 | 1, 3, 4 | 3bitri 195 | 1 ⊢ ((φ ∨ χ) ↔ (ψ ∨ χ)) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 98 ∨ wo 628 |
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-io 629 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: orbi12i 680 orordi 689 dcan 841 3or6 1217 19.45 1570 sbequilem 1716 unass 3094 frecsuc 5930 elznn0nn 8035 |
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