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Theorem dral2-o 34636
 Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). Version of dral2 2428 using ax-c11 34593. (Contributed by NM, 27-Feb-2005.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
dral2-o.1 (∀𝑥 𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
dral2-o (∀𝑥 𝑥 = 𝑦 → (∀𝑧𝜑 ↔ ∀𝑧𝜓))

Proof of Theorem dral2-o
StepHypRef Expression
1 hbae-o 34609 . 2 (∀𝑥 𝑥 = 𝑦 → ∀𝑧𝑥 𝑥 = 𝑦)
2 dral2-o.1 . 2 (∀𝑥 𝑥 = 𝑦 → (𝜑𝜓))
31, 2albidh 1906 1 (∀𝑥 𝑥 = 𝑦 → (∀𝑧𝜑 ↔ ∀𝑧𝜓))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196  ∀wal 1594 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-11 2147  ax-c5 34589  ax-c4 34590  ax-c7 34591  ax-c10 34592  ax-c11 34593  ax-c9 34596 This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1818 This theorem is referenced by:  ax12eq  34647  ax12el  34648  ax12indalem  34651  ax12inda2ALT  34652
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