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Theorem bnj1198 32783
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1198.1 (𝜑 → ∃𝑥𝜓)
bnj1198.2 (𝜓′𝜓)
Assertion
Ref Expression
bnj1198 (𝜑 → ∃𝑥𝜓′)

Proof of Theorem bnj1198
StepHypRef Expression
1 bnj1198.1 . 2 (𝜑 → ∃𝑥𝜓)
2 bnj1198.2 . . 3 (𝜓′𝜓)
32exbii 1850 . 2 (∃𝑥𝜓′ ↔ ∃𝑥𝜓)
41, 3sylibr 233 1 (𝜑 → ∃𝑥𝜓′)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205  wex 1782
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812
This theorem depends on definitions:  df-bi 206  df-ex 1783
This theorem is referenced by:  bnj1209  32784  bnj1275  32801  bnj1340  32811  bnj1345  32812  bnj605  32895  bnj607  32904  bnj906  32918  bnj908  32919  bnj1189  32997  bnj1450  33038  bnj1312  33046
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