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Theorem cutf 22
Description: Left-hand version of ax-cut 6.
Hypotheses
Ref Expression
cutf.1 (𝜓𝜑)
cutf.2 (~ 𝜓𝜒)
Assertion
Ref Expression
cutf (𝜒𝜑)

Proof of Theorem cutf
StepHypRef Expression
1 cutf.1 . . . 4 (𝜓𝜑)
21mdcoi 12 . . 3 (𝜑𝜓)
3 cutf.2 . . 3 (~ 𝜓𝜒)
42, 3ax-cut 6 . 2 (𝜑𝜒)
54mdcoi 12 1 (𝜒𝜑)
Colors of variables: wff var nilad
Syntax hints:  wmd 2  ~ wneg 3
This theorem was proved from axioms:  ax-ibot 4  ax-ebot 5  ax-cut 6  ax-mdco 8
This theorem is referenced by: (None)
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