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Mirrors > Home > ILE Home > Th. List > r19.37av | GIF version |
Description: Restricted version of one direction of Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 2-Apr-2004.) |
Ref | Expression |
---|---|
r19.37av | ⊢ (∃𝑥 ∈ 𝐴 (𝜑 → 𝜓) → (𝜑 → ∃𝑥 ∈ 𝐴 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | r19.37 2581 | 1 ⊢ (∃𝑥 ∈ 𝐴 (𝜑 → 𝜓) → (𝜑 → ∃𝑥 ∈ 𝐴 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wrex 2415 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-17 1506 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-ral 2419 df-rex 2420 |
This theorem is referenced by: ssiun 3850 |
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