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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 1823 | 1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1526 ∃wex 1771 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 |
This theorem depends on definitions: df-bi 208 df-ex 1772 |
This theorem is referenced by: eximi 1826 19.38b 1832 19.23v 1934 alequexv 1998 spsbeOLD 2080 nf5-1 2140 spimt 2395 darii 2745 festino 2754 baroco 2756 darapti 2764 elex2 3514 elex22 3515 vtoclegft 3579 spcimgft 3583 bj-axdd2 33823 bj-2exim 33842 bj-sylget 33851 bj-alexim 33857 bj-cbvalimt 33869 bj-cbveximt 33870 bj-eqs 33905 bj-nnf-exlim 33982 bj-nnflemee 33989 bj-nnflemae 33990 bj-axc10 34002 bj-alequex 34003 bj-spimtv 34013 bj-spcimdv 34108 bj-spcimdvv 34109 sn-el 38988 2exim 40588 pm11.71 40606 onfrALTlem2 40757 19.41rg 40761 ax6e2nd 40769 elex2VD 41049 elex22VD 41050 onfrALTlem2VD 41100 19.41rgVD 41113 ax6e2eqVD 41118 ax6e2ndVD 41119 ax6e2ndeqVD 41120 ax6e2ndALT 41141 ax6e2ndeqALT 41142 |
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