Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj937 Structured version   Visualization version   GIF version

Theorem bnj937 32117
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj937.1 (𝜑 → ∃𝑥𝜓)
Assertion
Ref Expression
bnj937 (𝜑𝜓)
Distinct variable group:   𝜓,𝑥
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem bnj937
StepHypRef Expression
1 bnj937.1 . 2 (𝜑 → ∃𝑥𝜓)
2 19.9v 1988 . 2 (∃𝑥𝜓𝜓)
31, 2sylib 221 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wex 1781
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970
This theorem depends on definitions:  df-bi 210  df-ex 1782
This theorem is referenced by:  bnj1265  32158  bnj1379  32176  bnj852  32267  bnj1148  32342  bnj1154  32345  bnj1189  32355  bnj1245  32360  bnj1286  32365  bnj1311  32370  bnj1371  32375  bnj1374  32377  bnj1498  32407  bnj1514  32409
  Copyright terms: Public domain W3C validator