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Theorem nfbidfOLD 2189
 Description: Obsolete proof of nfbidf 2079 as of 6-Oct-2021. (Contributed by Mario Carneiro, 4-Oct-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfbidfOLD.1 𝑥𝜑
nfbidfOLD.2 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
nfbidfOLD (𝜑 → (Ⅎ𝑥𝜓 ↔ Ⅎ𝑥𝜒))

Proof of Theorem nfbidfOLD
StepHypRef Expression
1 nfbidfOLD.1 . . 3 𝑥𝜑
2 nfbidfOLD.2 . . . 4 (𝜑 → (𝜓𝜒))
31, 2albidOLD 2187 . . . 4 (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒))
42, 3imbi12d 333 . . 3 (𝜑 → ((𝜓 → ∀𝑥𝜓) ↔ (𝜒 → ∀𝑥𝜒)))
51, 4albidOLD 2187 . 2 (𝜑 → (∀𝑥(𝜓 → ∀𝑥𝜓) ↔ ∀𝑥(𝜒 → ∀𝑥𝜒)))
6 df-nfOLD 1712 . 2 (Ⅎ𝑥𝜓 ↔ ∀𝑥(𝜓 → ∀𝑥𝜓))
7 df-nfOLD 1712 . 2 (Ⅎ𝑥𝜒 ↔ ∀𝑥(𝜒 → ∀𝑥𝜒))
85, 6, 73bitr4g 302 1 (𝜑 → (Ⅎ𝑥𝜓 ↔ Ⅎ𝑥𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195  ∀wal 1473  ℲwnfOLD 1700 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034 This theorem depends on definitions:  df-bi 196  df-ex 1696  df-nfOLD 1712 This theorem is referenced by: (None)
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