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Mirrors > Home > ILE Home > Th. List > 19.28v | GIF version |
Description: Theorem 19.28 of [Margaris] p. 90. (Contributed by NM, 25-Mar-2004.) |
Ref | Expression |
---|---|
19.28v | ⊢ (∀𝑥(𝜑 ∧ 𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1459 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | 1 | 19.28h 1494 | 1 ⊢ (∀𝑥(𝜑 ∧ 𝜓) ↔ (𝜑 ∧ ∀𝑥𝜓)) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 102 ↔ wb 103 ∀wal 1282 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-4 1440 ax-17 1459 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: reu6 2781 dfer2 6130 |
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