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| Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj524 | Structured version Visualization version GIF version | ||
| Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| bnj524.1 | ⊢ (𝜑 ↔ 𝜓) | 
| bnj524.2 | ⊢ 𝐴 ∈ V | 
| Ref | Expression | 
|---|---|
| bnj524 | ⊢ ([𝐴 / 𝑥]𝜑 ↔ [𝐴 / 𝑥]𝜓) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | bnj524.1 | . 2 ⊢ (𝜑 ↔ 𝜓) | |
| 2 | 1 | sbcbii 3845 | 1 ⊢ ([𝐴 / 𝑥]𝜑 ↔ [𝐴 / 𝑥]𝜓) | 
| Colors of variables: wff setvar class | 
| Syntax hints: ↔ wb 206 ∈ wcel 2107 Vcvv 3479 [wsbc 3787 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-8 2109 ax-9 2117 ax-ext 2707 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1542 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-sbc 3788 | 
| This theorem is referenced by: (None) | 
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