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Theorem foo3 29632
 Description: A theorem about the universal class. (Contributed by Stefan Allan, 9-Dec-2008.)
Hypothesis
Ref Expression
foo3.1 𝜑
Assertion
Ref Expression
foo3 V = {𝑥𝜑}

Proof of Theorem foo3
StepHypRef Expression
1 df-v 3342 . 2 V = {𝑥𝑥 = 𝑥}
2 equid 2094 . . . 4 𝑥 = 𝑥
3 foo3.1 . . . 4 𝜑
42, 32th 254 . . 3 (𝑥 = 𝑥𝜑)
54abbii 2877 . 2 {𝑥𝑥 = 𝑥} = {𝑥𝜑}
61, 5eqtri 2782 1 V = {𝑥𝜑}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1632  {cab 2746  Vcvv 3340 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-clab 2747  df-cleq 2753  df-clel 2756  df-v 3342 This theorem is referenced by: (None)
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