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Mirrors > Home > NFE 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 376 | . 2 ⊢ ((φ ∨ χ) ↔ (χ ∨ φ)) | |
2 | orbi2i.1 | . . 3 ⊢ (φ ↔ ψ) | |
3 | 2 | orbi2i 505 | . 2 ⊢ ((χ ∨ φ) ↔ (χ ∨ ψ)) |
4 | orcom 376 | . 2 ⊢ ((χ ∨ ψ) ↔ (ψ ∨ χ)) | |
5 | 1, 3, 4 | 3bitri 262 | 1 ⊢ ((φ ∨ χ) ↔ (ψ ∨ χ)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 ∨ wo 357 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-or 359 |
This theorem is referenced by: orbi12i 507 orordi 516 3anor 948 3or6 1263 19.45 1878 unass 3420 dfimak2 4298 ssfin 4470 eqtfinrelk 4486 evenoddnnnul 4514 nmembers1lem3 6270 nncdiv3 6277 nchoicelem6 6294 nchoicelem9 6297 nchoicelem18 6306 |
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