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Theorem bnj31 34712
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 3082 . 2 (∃𝑥𝐴 𝜓 → ∃𝑥𝐴 𝜒)
41, 3syl 17 1 (𝜑 → ∃𝑥𝐴 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wrex 3068
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-rex 3069
This theorem is referenced by:  bnj168  34723  bnj110  34851  bnj906  34923  bnj1253  35010  bnj1280  35013  bnj1296  35014  bnj1371  35022  bnj1497  35053  bnj1498  35054  bnj1501  35060
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