Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1265 Structured version   Visualization version   GIF version

Theorem bnj1265 32528
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj1265.1 (𝜑 → ∃𝑥𝐴 𝜓)
Assertion
Ref Expression
bnj1265 (𝜑𝜓)
Distinct variable group:   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝐴(𝑥)

Proof of Theorem bnj1265
StepHypRef Expression
1 bnj1265.1 . . . 4 (𝜑 → ∃𝑥𝐴 𝜓)
21bnj1196 32510 . . 3 (𝜑 → ∃𝑥(𝑥𝐴𝜓))
32bnj1266 32527 . 2 (𝜑 → ∃𝑥𝜓)
43bnj937 32487 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2111  wrex 3063
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1788  df-rex 3068
This theorem is referenced by:  bnj1253  32733  bnj1280  32736  bnj1296  32737  bnj1371  32745  bnj1497  32776
  Copyright terms: Public domain W3C validator