![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > mpsyl | GIF version |
Description: Modus ponens combined with a syllogism inference. (Contributed by Alan Sare, 20-Apr-2011.) |
Ref | Expression |
---|---|
mpsyl.1 | ⊢ φ |
mpsyl.2 | ⊢ (ψ → χ) |
mpsyl.3 | ⊢ (φ → (χ → θ)) |
Ref | Expression |
---|---|
mpsyl | ⊢ (ψ → θ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpsyl.1 | . . 3 ⊢ φ | |
2 | 1 | a1i 9 | . 2 ⊢ (ψ → φ) |
3 | mpsyl.2 | . 2 ⊢ (ψ → χ) | |
4 | mpsyl.3 | . 2 ⊢ (φ → (χ → θ)) | |
5 | 2, 3, 4 | sylc 56 | 1 ⊢ (ψ → θ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 |
This theorem is referenced by: relcnvtr 4783 relresfld 4790 relcoi1 4792 funco 4883 foimacnv 5087 fvi 5173 isoini2 5401 ovidig 5560 smores2 5850 tfrlem5 5871 cauappcvgprlemm 6617 caucvgprlemm 6639 |
Copyright terms: Public domain | W3C validator |