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Theorem rexbidvaALT 3278
 Description: Alternate proof of rexbidva 3255, shorter but requires more axioms. (Contributed by NM, 9-Mar-1997.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
rexbidvaALT.1 ((𝜑𝑥𝐴) → (𝜓𝜒))
Assertion
Ref Expression
rexbidvaALT (𝜑 → (∃𝑥𝐴 𝜓 ↔ ∃𝑥𝐴 𝜒))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)   𝐴(𝑥)

Proof of Theorem rexbidvaALT
StepHypRef Expression
1 nfv 1915 . 2 𝑥𝜑
2 rexbidvaALT.1 . 2 ((𝜑𝑥𝐴) → (𝜓𝜒))
31, 2rexbida 3277 1 (𝜑 → (∃𝑥𝐴 𝜓 ↔ ∃𝑥𝐴 𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209   ∧ wa 399   ∈ wcel 2111  ∃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  ax-5 1911  ax-6 1970  ax-7 2015  ax-12 2175 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-nf 1786  df-rex 3112 This theorem is referenced by: (None)
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