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Theorem orbi1i 506

Description: Inference adding a right disjunct to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.)

**Hypothesis**
Ref	Expression
orbi2i.1	⊢ (φ ↔ ψ)

**Assertion**
Ref	Expression
orbi1i	⊢ ((φ ∨ χ) ↔ (ψ ∨ χ))

**Proof of Theorem orbi1i**
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-1 5 ax-2 6 ax-3 7 ax-mp 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