Theorem bnj524 34872

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 3796	1 ⊢ ([𝐴 / 𝑥]𝜑 ↔ [𝐴 / 𝑥]𝜓)

Syntax hints:   ↔ wb 206   ∈ wcel 2114  Vcvv 3439  [wsbc 3739

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2714  df-cleq 2727  df-clel 2810  df-sbc 3740

This theorem is referenced by: (None)