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Theorem spimvALT 2294
Description: Alternate proof of spimv 2293. Shorter but requires more axioms. (Contributed by NM, 31-Jul-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
spimv.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
spimvALT (∀𝑥𝜑𝜓)
Distinct variable group:   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑦)

Proof of Theorem spimvALT
StepHypRef Expression
1 nfv 1883 . 2 𝑥𝜓
2 spimv.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
31, 2spim 2290 1 (∀𝑥𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-12 2087  ax-13 2282
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745  df-nf 1750
This theorem is referenced by: (None)
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