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Theorem mdm2s 74
Description: Par is monotone in its second argument. Syllogism form of mdm2 69.
Hypothesis
Ref Expression
mdm2s.1 (𝜓𝜒)
Assertion
Ref Expression
mdm2s ((𝜑𝜓) ⊸ (𝜑𝜒))

Proof of Theorem mdm2s
StepHypRef Expression
1 ax-init 7 . . 3 (~ (𝜑𝜓) ⅋ (𝜑𝜓))
2 mdm2s.1 . . 3 (𝜓𝜒)
31, 2mdm2 69 . 2 (~ (𝜑𝜓) ⅋ (𝜑𝜒))
43dfli2i 66 1 ((𝜑𝜓) ⊸ (𝜑𝜒))
Colors of variables: wff var nilad
Syntax hints:  wmd 2  ~ wneg 3  wli 61
This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-init 7  ax-mdco 8  ax-mdas 9  ax-eac1 33  ax-eac2 34
This theorem depends on definitions:  df-lb 56  df-li 62
This theorem is referenced by:  licon  94
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