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Theorem bnj31 31115
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 3149 . 2 (∃𝑥𝐴 𝜓 → ∃𝑥𝐴 𝜒)
41, 3syl 17 1 (𝜑 → ∃𝑥𝐴 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wrex 3051
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854  df-ral 3055  df-rex 3056
This theorem is referenced by:  bnj168  31126  bnj110  31256  bnj906  31328  bnj1253  31413  bnj1280  31416  bnj1296  31417  bnj1371  31425  bnj1497  31456  bnj1498  31457  bnj1501  31463
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