Theorem bnj524 35368

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 3794	1 ⊢ ([𝐴 / 𝑥]𝜑 ↔ [𝐴 / 𝑥]𝜓)

This proof depends on syntax axioms:   ↔ wb 209   ∈ wcel 2144  Vcvv 3450  [wsbc 3738

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-sbc 3739

This theorem is used by: (None)