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Mirrors > Home > NFE Home > Th. List > r19.37av | GIF version |
Description: Restricted version of one direction of Theorem 19.37 of [Margaris] p. 90. (The other direction doesn't hold when A is empty.) (Contributed by NM, 2-Apr-2004.) |
Ref | Expression |
---|---|
r19.37av | ⊢ (∃x ∈ A (φ → ψ) → (φ → ∃x ∈ A ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1619 | . 2 ⊢ Ⅎxφ | |
2 | 1 | r19.37 2760 | 1 ⊢ (∃x ∈ A (φ → ψ) → (φ → ∃x ∈ A ψ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wrex 2615 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-11 1746 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-ral 2619 df-rex 2620 |
This theorem is referenced by: ssiun 4008 |
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