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Theorem ccase2 1024
Description: Inference for combining cases. (Contributed by NM, 29-Jul-1999.)
Hypotheses
Ref Expression
ccase2.1 ((𝜑𝜓) → 𝜏)
ccase2.2 (𝜒𝜏)
ccase2.3 (𝜃𝜏)
Assertion
Ref Expression
ccase2 (((𝜑𝜒) ∧ (𝜓𝜃)) → 𝜏)

Proof of Theorem ccase2
StepHypRef Expression
1 ccase2.1 . 2 ((𝜑𝜓) → 𝜏)
2 ccase2.2 . . 3 (𝜒𝜏)
32adantr 466 . 2 ((𝜒𝜓) → 𝜏)
4 ccase2.3 . . 3 (𝜃𝜏)
54adantl 467 . 2 ((𝜑𝜃) → 𝜏)
64adantl 467 . 2 ((𝜒𝜃) → 𝜏)
71, 3, 5, 6ccase 1022 1 (((𝜑𝜒) ∧ (𝜓𝜃)) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wo 826
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827
This theorem is referenced by:  opthhausdorff  5110  fctop  21028  cctop  21030
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