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41.    p a (q a r) —* (p a q) a r

D o w ód. 16 :: 7 q/q a r =>7 p/g, r//r =>(1)

(1)    p a (q a r) —♦ r

16 :: 7 q/q a r=> 6 pfq. q/r =>(2)

(2)    p a {q a r) —* q

8 :: 6 qfq a r => (2) => (3)

(3)    p a (q a r) - p a q

16 :: (3)=> 31 p/p a q, ąfr =>(4)

(4)    p a {(/ a r) -* [r -* (p a q) a r]

2 :: (4)=>(1)=>41

§ 5. TEZY ZE ZNAKIEM ALTERNATYWY

42.    p v q-*q v p

D o w ó d. 11 r/q v p :: 10 ^/p. p/<? =*9 p/g, <j/p =>42

43.    (p v q) v r-* p v (q v r)

Dowód. 16 :: 9 pjq, ąfr =>10 qfq v r =» (1)

(1)    </ — P v (</ v r)

11 r/p v (4 v r) :: 9 qfą v r =>(1)=>(2)

(2)    pvq-»p v(qvr)

16 :: 10 r//r, p/</ => 10 v r =>(3)

(3)    r -> p v v r)

11 :: (2)=>(3)=>43

44.    p v (g v r) -»(p v ą) v r

Dowód. 16 :: 9 => 9 p/p v q, <//r ==>(!)

(1) P -> (p v q) v r

16 :: 10=>9 p/p v q, q/r =>(2)