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Theorem rexeqOLD 3416
 Description: Obsolete version of rexeq 3412 as of 5-May-2023. Equality theorem for restricted existential quantifier. (Contributed by NM, 29-Oct-1995.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
rexeqOLD (𝐴 = 𝐵 → (∃𝑥𝐴 𝜑 ↔ ∃𝑥𝐵 𝜑))
Distinct variable groups:   𝑥,𝐴   𝑥,𝐵
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem rexeqOLD
StepHypRef Expression
1 nfcv 2982 . 2 𝑥𝐴
2 nfcv 2982 . 2 𝑥𝐵
31, 2rexeqf 3404 1 (𝐴 = 𝐵 → (∃𝑥𝐴 𝜑 ↔ ∃𝑥𝐵 𝜑))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 207   = wceq 1530  ∃wrex 3144 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2153  ax-12 2169  ax-ext 2798 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-cleq 2819  df-clel 2898  df-nfc 2968  df-rex 3149 This theorem is referenced by: (None)
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