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Mirrors > Home > ILE Home > Th. List > or4 | GIF version |
Description: Rearrangement of 4 disjuncts. (Contributed by NM, 12-Aug-1994.) |
Ref | Expression |
---|---|
or4 | ⊢ (((φ ∨ ψ) ∨ (χ ∨ θ)) ↔ ((φ ∨ χ) ∨ (ψ ∨ θ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | or12 682 | . . 3 ⊢ ((ψ ∨ (χ ∨ θ)) ↔ (χ ∨ (ψ ∨ θ))) | |
2 | 1 | orbi2i 678 | . 2 ⊢ ((φ ∨ (ψ ∨ (χ ∨ θ))) ↔ (φ ∨ (χ ∨ (ψ ∨ θ)))) |
3 | orass 683 | . 2 ⊢ (((φ ∨ ψ) ∨ (χ ∨ θ)) ↔ (φ ∨ (ψ ∨ (χ ∨ θ)))) | |
4 | orass 683 | . 2 ⊢ (((φ ∨ χ) ∨ (ψ ∨ θ)) ↔ (φ ∨ (χ ∨ (ψ ∨ θ)))) | |
5 | 2, 3, 4 | 3bitr4i 201 | 1 ⊢ (((φ ∨ ψ) ∨ (χ ∨ θ)) ↔ ((φ ∨ χ) ∨ (ψ ∨ θ))) |
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: or42 688 orordi 689 orordir 690 3or6 1217 swoer 6070 apcotr 7391 |
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