Theorem bnj524 31324

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypotheses

Ref	Expression
bnj524.1	⊢ (𝜑 ↔ 𝜓)
bnj524.2	⊢ 𝐴 ∈ V

Assertion

Ref	Expression
bnj524	⊢ ([𝐴 / 𝑥]𝜑 ↔ [𝐴 / 𝑥]𝜓)

Proof of Theorem bnj524

Step	Hyp	Ref	Expression
1		bnj524.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2	1	sbcbii 3689	1 ⊢ ([𝐴 / 𝑥]𝜑 ↔ [𝐴 / 𝑥]𝜓)

Syntax hints:   ↔ wb 198   ∈ wcel 2157  Vcvv 3385  [wsbc 3633

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-ext 2777

This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-sbc 3634

This theorem is referenced by: (None)