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Mirrors > Home > MPE Home > Th. List > exim | Structured version Visualization version GIF version |
Description: Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 10-Jan-1993.) (Proof shortened by Wolf Lammen, 4-Jul-2014.) |
Ref | Expression |
---|---|
exim | ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓)) | |
2 | 1 | aleximi 1829 | 1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1535 ∃wex 1776 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 |
This theorem depends on definitions: df-bi 207 df-ex 1777 |
This theorem is referenced by: eximi 1832 19.38b 1838 19.23v 1940 alequexv 1998 nf5-1 2143 spimt 2389 darii 2663 festino 2672 baroco 2674 darapti 2682 elex2OLD 3503 elex22 3504 spcimgfi1OLD 3548 vtoclegftOLD 3589 sbccomlem 3878 rspn0 4362 exel 5444 bj-axdd2 36575 bj-2exim 36594 bj-sylget 36604 bj-alexim 36610 bj-cbvalimt 36622 bj-cbveximt 36623 bj-eqs 36658 bj-nnf-exlim 36739 bj-nnflemee 36746 bj-nnflemae 36747 bj-axc10 36766 bj-alequex 36767 bj-spimtv 36777 bj-spcimdv 36878 bj-spcimdvv 36879 sn-exelALT 42236 2exim 44375 pm11.71 44393 onfrALTlem2 44544 19.41rg 44548 ax6e2nd 44556 elex2VD 44836 elex22VD 44837 onfrALTlem2VD 44887 19.41rgVD 44900 ax6e2eqVD 44905 ax6e2ndVD 44906 ax6e2ndeqVD 44907 ax6e2ndALT 44928 ax6e2ndeqALT 44929 |
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