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Mirrors > Home > NFE Home > Th. List > com15 | GIF version |
Description: Commutation of antecedents. Swap 1st and 5th. (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 |
---|---|
com15 | ⊢ (τ → (ψ → (χ → (θ → (φ → η))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | com5.1 | . . 3 ⊢ (φ → (ψ → (χ → (θ → (τ → η))))) | |
2 | 1 | com5l 86 | . 2 ⊢ (ψ → (χ → (θ → (τ → (φ → η))))) |
3 | 2 | com4r 80 | 1 ⊢ (τ → (ψ → (χ → (θ → (φ → η))))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 8 |
This theorem is referenced by: (None) |
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