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Axiom ax-arg 1151
Description: The Arguesian law as an axiom.
Hypothesis
Ref Expression
arg.1 ((a0 v b0) ^ (a1 v b1)) =< (a2 v b2)
Assertion
Ref Expression
ax-arg ((a0 v a1) ^ (b0 v b1)) =< (((a0 v a2) ^ (b0 v b2)) v ((a1 v a2) ^ (b1 v b2)))

Detailed syntax breakdown of Axiom ax-arg
StepHypRef Expression
1 wva0 . . . 4 term a0
2 wva1 . . . 4 term a1
31, 2wo 6 . . 3 term (a0 v a1)
4 wvb0 . . . 4 term b0
5 wvb1 . . . 4 term b1
64, 5wo 6 . . 3 term (b0 v b1)
73, 6wa 7 . 2 term ((a0 v a1) ^ (b0 v b1))
8 wva2 . . . . 5 term a2
91, 8wo 6 . . . 4 term (a0 v a2)
10 wvb2 . . . . 5 term b2
114, 10wo 6 . . . 4 term (b0 v b2)
129, 11wa 7 . . 3 term ((a0 v a2) ^ (b0 v b2))
132, 8wo 6 . . . 4 term (a1 v a2)
145, 10wo 6 . . . 4 term (b1 v b2)
1513, 14wa 7 . . 3 term ((a1 v a2) ^ (b1 v b2))
1612, 15wo 6 . 2 term (((a0 v a2) ^ (b0 v b2)) v ((a1 v a2) ^ (b1 v b2)))
177, 16wle 2 1 wff ((a0 v a1) ^ (b0 v b1)) =< (((a0 v a2) ^ (b0 v b2)) v ((a1 v a2) ^ (b1 v b2)))
Colors of variables: term
This axiom is referenced by:  dp15lemb  1153  xdp15  1197  xxdp15  1200
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