Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1238 Structured version   Visualization version   GIF version

Theorem bnj1238 31205
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1238.1 (𝜑 ↔ ∃𝑥𝐴 (𝜓𝜒))
Assertion
Ref Expression
bnj1238 (𝜑 → ∃𝑥𝐴 𝜓)

Proof of Theorem bnj1238
StepHypRef Expression
1 bnj1238.1 . 2 (𝜑 ↔ ∃𝑥𝐴 (𝜓𝜒))
2 bnj1239 31204 . 2 (∃𝑥𝐴 (𝜓𝜒) → ∃𝑥𝐴 𝜓)
31, 2sylbi 207 1 (𝜑 → ∃𝑥𝐴 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 383  wrex 3051
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854  df-ral 3055  df-rex 3056
This theorem is referenced by:  bnj1245  31410  bnj1256  31411  bnj1259  31412  bnj1311  31420  bnj1371  31425
  Copyright terms: Public domain W3C validator