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Mirrors > Home > NFE Home > Th. List > com24 | GIF version |
Description: Commutation of antecedents. Swap 2nd and 4th. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.) |
Ref | Expression |
---|---|
com4.1 | ⊢ (φ → (ψ → (χ → (θ → τ)))) |
Ref | Expression |
---|---|
com24 | ⊢ (φ → (θ → (χ → (ψ → τ)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | com4.1 | . . 3 ⊢ (φ → (ψ → (χ → (θ → τ)))) | |
2 | 1 | com4t 79 | . 2 ⊢ (χ → (θ → (φ → (ψ → τ)))) |
3 | 2 | com13 74 | 1 ⊢ (φ → (θ → (χ → (ψ → τ)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: com25 85 nclenn 6249 |
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