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Theorem cbvsbcv 3617
 Description: Change the bound variable of a class substitution using implicit substitution. (Contributed by NM, 30-Sep-2008.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypothesis
Ref Expression
cbvsbcv.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
cbvsbcv ([𝐴 / 𝑥]𝜑[𝐴 / 𝑦]𝜓)
Distinct variable groups:   𝜑,𝑦   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)   𝐴(𝑥,𝑦)

Proof of Theorem cbvsbcv
StepHypRef Expression
1 nfv 1995 . 2 𝑦𝜑
2 nfv 1995 . 2 𝑥𝜓
3 cbvsbcv.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
41, 2, 3cbvsbc 3616 1 ([𝐴 / 𝑥]𝜑[𝐴 / 𝑦]𝜓)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 196  [wsbc 3587 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-sbc 3588 This theorem is referenced by:  fpwwe2cbv  9654
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