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Theorem bnj1224 31381
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1224.1 ¬ (𝜃𝜏𝜂)
Assertion
Ref Expression
bnj1224 ((𝜃𝜏) → ¬ 𝜂)

Proof of Theorem bnj1224
StepHypRef Expression
1 bnj1224.1 . . 3 ¬ (𝜃𝜏𝜂)
2 df-3an 1110 . . 3 ((𝜃𝜏𝜂) ↔ ((𝜃𝜏) ∧ 𝜂))
31, 2mtbi 314 . 2 ¬ ((𝜃𝜏) ∧ 𝜂)
43imnani 390 1 ((𝜃𝜏) → ¬ 𝜂)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 385  w3a 1108
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 199  df-an 386  df-3an 1110
This theorem is referenced by:  bnj1204  31589  bnj1279  31595
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