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Mirrors > Home > ILE Home > Th. List > mpan9 | Unicode version |
Description: Modus ponens conjoining dissimilar antecedents. (Contributed by NM, 1-Feb-2008.) (Proof shortened by Andrew Salmon, 7-May-2011.) |
Ref | Expression |
---|---|
mpan9.1 | |
mpan9.2 |
Ref | Expression |
---|---|
mpan9 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpan9.1 | . . 3 | |
2 | mpan9.2 | . . 3 | |
3 | 1, 2 | syl5 28 | . 2 |
4 | 3 | impcom 116 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 |
This theorem is referenced by: sylan 267 vtocl2gf 2615 vtocl3gf 2616 vtoclegft 2625 sbcthdv 2778 swopolem 4042 funssres 4942 fvmptssdm 5255 fmptcof 5331 fliftfuns 5438 isorel 5448 caovclg 5653 caovcomg 5656 caovassg 5659 caovcang 5662 caovordig 5666 caovordg 5668 caovdig 5675 caovdirg 5678 qliftfuns 6190 nneneq 6320 recexprlemopl 6723 recexprlemopu 6725 cauappcvgprlemladdrl 6755 caucvgsrlemcl 6873 caucvgsrlemfv 6875 caucvgsr 6886 uz11 8495 iseqfeq 9231 iseqcaopr3 9240 climcaucn 9870 |
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