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Mirrors > Home > NFE Home > Th. List > ralrimivw | GIF version |
Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 18-Jun-2014.) |
Ref | Expression |
---|---|
ralrimivw.1 | ⊢ (φ → ψ) |
Ref | Expression |
---|---|
ralrimivw | ⊢ (φ → ∀x ∈ A ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralrimivw.1 | . . 3 ⊢ (φ → ψ) | |
2 | 1 | a1d 22 | . 2 ⊢ (φ → (x ∈ A → ψ)) |
3 | 2 | ralrimiv 2696 | 1 ⊢ (φ → ∀x ∈ A ψ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 1710 ∀wral 2614 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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-ex 1542 df-nf 1545 df-ral 2619 |
This theorem is referenced by: 2rmorex 3040 riinrab 4041 nnadjoinpw 4521 dmxp 4923 eqfnfv 5392 mpteq12dv 5656 mpt2eq12 5662 clos1nrel 5886 uniqs 5984 enprmaplem5 6080 nchoicelem6 6294 dmfrec 6316 |
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