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Theorem acm1i 82
Description: With is monotone in its first argument. Inference form of acm1 80.
Hypotheses
Ref Expression
acm1i.1 (𝜑 & 𝜓)
acm1i.2 (𝜑𝜒)
Assertion
Ref Expression
acm1i (𝜒 & 𝜓)

Proof of Theorem acm1i
StepHypRef Expression
1 acm1i.1 . . . 4 (𝜑 & 𝜓)
21ax-ibot 4 . . 3 (⊥ ⅋ (𝜑 & 𝜓))
3 acm1i.2 . . 3 (𝜑𝜒)
42, 3acm1 80 . 2 (⊥ ⅋ (𝜒 & 𝜓))
54ax-ebot 5 1 (𝜒 & 𝜓)
Colors of variables: wff var nilad
Syntax hints:  wbot 1   & wac 30  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-iac 32  ax-eac1 33  ax-eac2 34
This theorem depends on definitions:  df-lb 56  df-li 62
This theorem is referenced by: (None)
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