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Mirrors > Home > NFE Home > Th. List > com5l | GIF version |
Description: Commutation of antecedents. Rotate left. (Contributed by Jeff Hankins, 28-Jun-2009.) (Proof shortened by Wolf Lammen, 29-Jul-2012.) |
Ref | Expression |
---|---|
com5.1 | ⊢ (φ → (ψ → (χ → (θ → (τ → η))))) |
Ref | Expression |
---|---|
com5l | ⊢ (ψ → (χ → (θ → (τ → (φ → η))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | com5.1 | . . 3 ⊢ (φ → (ψ → (χ → (θ → (τ → η))))) | |
2 | 1 | com4l 78 | . 2 ⊢ (ψ → (χ → (θ → (φ → (τ → η))))) |
3 | 2 | com45 83 | 1 ⊢ (ψ → (χ → (θ → (τ → (φ → η))))) |
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: com15 87 com52l 88 com52r 89 |
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