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Theorem mdm1 70
Description: Par is monotone in its first argument.
Hypotheses
Ref Expression
mdm1.1 (𝜃 ⅋ (𝜑𝜓))
mdm1.2 (𝜑𝜒)
Assertion
Ref Expression
mdm1 (𝜃 ⅋ (𝜒𝜓))

Proof of Theorem mdm1
StepHypRef Expression
1 mdm1.1 . . . 4 (𝜃 ⅋ (𝜑𝜓))
21mdcod 11 . . 3 (𝜃 ⅋ (𝜓𝜑))
3 mdm1.2 . . 3 (𝜑𝜒)
42, 3mdm2 69 . 2 (𝜃 ⅋ (𝜓𝜒))
54mdcod 11 1 (𝜃 ⅋ (𝜒𝜓))
Colors of variables: wff var nilad
Syntax hints:  wmd 2  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
This theorem depends on definitions:  df-lb 56  df-li 62
This theorem is referenced by:  mdm1i  71  mdm1s  73
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