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Theorem bnj1198 32141
 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 1849 . 2 (∃𝑥𝜓′ ↔ ∃𝑥𝜓)
41, 3sylibr 237 1 (𝜑 → ∃𝑥𝜓′)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ 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:  bnj1209  32142  bnj1275  32159  bnj1340  32169  bnj1345  32170  bnj605  32253  bnj607  32262  bnj906  32276  bnj908  32277  bnj1189  32355  bnj1450  32396  bnj1312  32404
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