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Theorem bnj133 32057
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj133.1 (𝜑 ↔ ∃𝑥𝜓)
bnj133.2 (𝜒𝜓)
Assertion
Ref Expression
bnj133 (𝜑 ↔ ∃𝑥𝜒)

Proof of Theorem bnj133
StepHypRef Expression
1 bnj133.1 . 2 (𝜑 ↔ ∃𝑥𝜓)
2 bnj133.2 . . 3 (𝜒𝜓)
32exbii 1849 . 2 (∃𝑥𝜒 ↔ ∃𝑥𝜓)
41, 3bitr4i 281 1 (𝜑 ↔ ∃𝑥𝜒)
Colors of variables: wff setvar class
Syntax hints:  wb 209  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
This theorem depends on definitions:  df-bi 210  df-ex 1782
This theorem is referenced by:  bnj150  32208  bnj983  32283  bnj984  32284  bnj985v  32285  bnj985  32286  bnj1090  32311  bnj1514  32395
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