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Theorem bnj1219 29918
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1219.1 (𝜒 ↔ (𝜑𝜓𝜁))
bnj1219.2 (𝜃 ↔ (𝜒𝜏𝜂))
Assertion
Ref Expression
bnj1219 (𝜃𝜓)

Proof of Theorem bnj1219
StepHypRef Expression
1 bnj1219.2 . 2 (𝜃 ↔ (𝜒𝜏𝜂))
2 bnj1219.1 . . 3 (𝜒 ↔ (𝜑𝜓𝜁))
32simp2bi 1069 . 2 (𝜒𝜓)
41, 3bnj835 29876 1 (𝜃𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  w3a 1030
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 195  df-an 384  df-3an 1032
This theorem is referenced by:  bnj1379  29948
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