Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1196 Structured version   Visualization version   GIF version

Theorem bnj1196 32176
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1196.1 (𝜑 → ∃𝑥𝐴 𝜓)
Assertion
Ref Expression
bnj1196 (𝜑 → ∃𝑥(𝑥𝐴𝜓))

Proof of Theorem bnj1196
StepHypRef Expression
1 bnj1196.1 . 2 (𝜑 → ∃𝑥𝐴 𝜓)
2 df-rex 3112 . 2 (∃𝑥𝐴 𝜓 ↔ ∃𝑥(𝑥𝐴𝜓))
31, 2sylib 221 1 (𝜑 → ∃𝑥(𝑥𝐴𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  wex 1781  wcel 2111  wrex 3107
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 210  df-rex 3112
This theorem is referenced by:  bnj1209  32178  bnj1265  32194  bnj1379  32212  bnj1521  32233  bnj900  32311  bnj986  32337  bnj1189  32391  bnj1245  32396  bnj1286  32401  bnj1311  32406  bnj1450  32432  bnj1498  32443
  Copyright terms: Public domain W3C validator