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Theorem bnj31 32114
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj31.1 (𝜑 → ∃𝑥𝐴 𝜓)
bnj31.2 (𝜓𝜒)
Assertion
Ref Expression
bnj31 (𝜑 → ∃𝑥𝐴 𝜒)

Proof of Theorem bnj31
StepHypRef Expression
1 bnj31.1 . 2 (𝜑 → ∃𝑥𝐴 𝜓)
2 bnj31.2 . . 3 (𝜓𝜒)
32reximi 3206 . 2 (∃𝑥𝐴 𝜓 → ∃𝑥𝐴 𝜒)
41, 3syl 17 1 (𝜑 → ∃𝑥𝐴 𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wrex 3107 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-an 400  df-ex 1782  df-ral 3111  df-rex 3112 This theorem is referenced by:  bnj168  32125  bnj110  32255  bnj906  32327  bnj1253  32414  bnj1280  32417  bnj1296  32418  bnj1371  32426  bnj1497  32457  bnj1498  32458  bnj1501  32464
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