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Theorem drex2 2463
 Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). (Contributed by NM, 27-Feb-2005.)
Hypothesis
Ref Expression
dral1.1 (∀𝑥 𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
drex2 (∀𝑥 𝑥 = 𝑦 → (∃𝑧𝜑 ↔ ∃𝑧𝜓))

Proof of Theorem drex2
StepHypRef Expression
1 nfae 2453 . 2 𝑧𝑥 𝑥 = 𝑦
2 dral1.1 . 2 (∀𝑥 𝑥 = 𝑦 → (𝜑𝜓))
31, 2exbid 2266 1 (∀𝑥 𝑥 = 𝑦 → (∃𝑧𝜑 ↔ ∃𝑧𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 198  ∀wal 1654  ∃wex 1878 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-10 2192  ax-11 2207  ax-12 2220  ax-13 2389 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883 This theorem is referenced by:  dfid3  5253  dropab1  39488  dropab2  39489  e2ebind  39606
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